Romana has managed to convince the temporal powers to attend a summit to discuss and agree upon legislation to limit time travel within the Vortex. Despite the devastating events that took place during the last summit, Gallifrey’s refusal to use force against Gryben has convinced the other temporal powers that the Time Lords’ intentions are peaceable. For the benefit of Cardinal Braxiatel, who has been busy elsewhere, Liaison Officer Hossak explains that the temporal powers have jointly designed and constructed a synthetic planetoid within neutral space, protected by a temporal force field and staffed exclusively by automated servitors slaved to a central network and monitored by representatives of every temporal power. Any attempt to interfere with their programming will cause the servitors to shut down and reboot, and will instantly be detected by the other temporal powers. Only lesser politicians will be attending the summit in person; the heads of state will communicate via holographic projections. Romana orders Co-ordinator Narvin to represent Gallifrey at the summit, much to his displeasure.
Leela is aware that Romana is hiding something important, and Romana admits that she fears that whoever supplied the timonic fusion device to Free Time may try to take advantage of the summit to drive another wedge between the Time Lords and the other temporal powers. Hossak is wholly committed to the cause of peace, but she’s perhaps a bit too trusting; thus, Romana sends in Leela undercover, as an exotic dancer. The more serious the purpose of the summit, the more serious the delegates are about “unwinding” afterwards, and each delegate has been permitted to select their own personal entertainers. Leela reluctantly accepts the mission, and travels to the planet with the other dancers, including young Lexy and the experienced Baano, who was selected by Flinkstab of Nekkistan and who can barely fit into the shuttle along with the luggage containing all of the costumes for her act. Leela is accompanied by K9 Mark I, and although the servitors remove his blaster and fit his sensors with limiters, he surreptitiously remains linked to K9 Mark II back on Gallifrey. Together, they will monitor the network for any wrongdoing.
Hossak welcomes the delegates to the summit, including Narvin, V’rell of the Monan Host, Flinkstab of the Nekkistani, and Pule of Unvoss, amongst others. Sadly, the delegates soon engage in petty political bickering; Narvin advocates leaving unstable areas of the time continuum alone, and V’rell and Flinkstab suggest that this is because the Time Lords fear that other races will learn of their past mistakes. Narvin points out that the Monan Host world was created due to a temporal accident, and that any meddling could erase it from history; in turn, V’rell accuses the Time Lords of offering “help” to the Monan Host after the Dalek invasion of their homeworld simply so the Gallifreyans could learn the secrets of the Monan timeships. Romana appears via hologram to break up the squabbling, and as the day draws to a close, Hossak suggests that the delegates relax and reconvene tomorrow in better spirits. Elsewhere, Romana leaves K9-II with six pre-recorded, generic speeches to play back for the delegates as he deems appropriate, while she sets off in the Presidential TARDIS to conduct important business elsewhere.
Over drinks, Narvin and Flinkstab discuss the nature of the Monan Host world. Though the Monans have generated an occlusion field to prevent other temporal powers from peering back into their history, the Nekkistani have learned that some incident caused time and space to buckle around the Monan homeworld, putting it in contact with itself in ten different historical periods. The most advanced Monans conquered their ancestors, studied and harnessed the time fields, and stabilised the ten planets into a single host system. All attempts to replicate the Monans’ technology have failed. Narvin suggests that, should some unfortunate accident happen to erase the Monan Host from the time continuum, this would leave a power vacuum which the Nekkistani and Time Lords would be well-placed to fill. Flinkstab promises to consider this interesting proposal, but first he intends to unwind and forget the petty nuisances of this poorly-organised summit -- such as the fact that an entire consignment of the servitors seems to have gone missing.
Leela searches the dancers’ quarters but finds nothing of interest. K9-I contacts his counterpart and receives the codes she will need to enter the delegates’ rooms, but she can’t take advantage of them until the delegates are back at the summit tomorrow. Baano and Lexy then arrive with Flinkstab, who has been ogling Leela and now demands that she put on a private show for him. When she refuses, he tries to force her, but she easily overpowers him and drives him from the room. He leaves vowing to have his fun with her. Leela is not concerned, but later, when she visits the showers, she finds Lexy dead. A servitor finds Leela standing over Lexy’s mutilated body and places her under arrest; as she is dragged off to the holding cells, Leela orders K9-I to search Flinkstab’s quarters, certain that he is responsible. Hossak then confronts Leela, enraged; she’d only accepted Leela’s presence at the summit to demonstrate to the other delegates that the Time Lords have a progressive attitude towards the lesser species, and now Leela has linked Gallifrey to a sordid scandal. The other delegates may now lose their respect for Gallifrey, and all of Hossak’s hard work organising this summit will be for nothing. Hossak leaves Leela locked up in the holding cell, but as Leela protests her innocence, something strange happens to Time...
It is the previous day again, and Leela, K9-I and the other dancers -- including Lexy -- are being shown to their rooms by the servitors. This time around, Narvin chokes on his drink while speaking with V’rell and Flinkstab, and the ensuing argument never takes place; thus, Romana is forced to leave Gallifrey without the opportunity to try out her pre-recorded speech. Leela experiences a strange sense of déjŕ vu, and decides to search the delegates’ rooms before the summit is over -- and in Flinkstab’s rooms, she finds holo-prints of Lexy’s mutilated body. But Lexy is still alive and the time code indicates that the prints will not be taken for hours, even though none of the temporal powers have detected temporal fluctuations within the network. Leela has K9-I inform his counterpart, and Romana decides to investigate in person. She thus leaves Braxiatel in charge and bids goodbye to the High Monan -- and all others attending this important meeting.
That night, Leela dances with the others in order to keep an eye on Lexy and Flinkstab. Baano, though impressed with Leela’s skills, takes her leave when Flinkstab becomes too appreciative. Narvin watches from the sidelines, displeased with this whole affair and convinced that the other delegates are only here to learn Gallifrey’s secrets -- just as he’s here to learn theirs. Still, at least he knows how to deal with the Monans if it becomes necessary... As Narvin speaks with Pule of Unvoss, a servitor arrives and offers Pule a drink -- which explodes, killing Pule. The other delegates turn on Narvin, accusing him of killing Pule, and though Narvin insists that the real assassin was a servitor, he can’t identify the one in question -- and since no fluctuations in the servitors’ network have been detected, nobody believes him. In the confusion, Narvin finds that Hossak has abandoned him to face the angry delegates alone, and Leela realises that Baano, Lexy and Flinkstab are nowhere to be seen either. But as Leela and K9-I set off to find and save Lexy, Time goes into reverse once again.
This time around, however, when the servitors show Leela and K9-I to their rooms, Leela realises that she’s been through all of this before. She can remember Lexy’s and Pule’s deaths -- and she still has the holo-prints depicting Lexy’s murder -- yet both are still alive. Leela tries to explain the danger to Baano, but Baano scoffs, particularly when Leela claims that she’s personal friends with President Romana, who is on her way to sort everything out.
Romana has some trouble passing through the planetoid’s defence shield, as it seems that she’s failed to clear her central command. When her TARDIS materialises, nobody is there to greet her, and when the flustered Hossak arrives she doesn’t seem to have been expecting Romana’s arrival. Romana realises that Time has gone into reverse again, and tries to warn Hossak that someone is turning back Time to ensure that events at the summit run to a predetermined course; but Hossak points out that the network has detected no such tampering, and advises Romana to keep her theory to herself lest she alarm the other delegates.
Irritated, Romana sets off to find Leela, but is unexpectedly attacked by a servitor which does not seem to be following strictly logical attack patterns. This should be impossible, but none of the monitoring powers seem to have noticed the servitor’s behaviour and it’s not shutting down. At the last moment, Leela arrives and even more unexpectedly knocks the servitor unconscious -- thus proving that it’s not a robot after all. Romana’s attacker turns out to be Baano, who must have smuggled this disguise into the summit in pieces amongst her other costumes. Since Flinkstab is the one who arranged for Baano to attend the summit, Leela and Romana conclude that he’s trying to drive a wedge between Gallifrey and the other temporal powers to make Nekkistani look like a more attractive ally. This must be why Narvin was framed for Pule’s murder the last time around, but this time, when Leela told Baano that Romana was on her way, she must have decided to frame the Time Lord President herself for the murder.
Romana and Leela thus drag Baano to Flinkstab’s quarters and demand an explanation of him. Leela accuses Flinkstab of slaughtering a helpless dancing girl, and before Romana can remind her that Lexy has not been killed this time around, Flinkstab collapses in tears, insisting that the girl on Coralee just wanted to have fun with him. Leela, disgusted, realises that Flinkstab has killed before, and that his tears now are just from terror that he’s been caught out. However, he’s just a perverted sadist, not a political assassin, who was manipulated into selecting Baano for this gig. When Baano awakens, she reveals that her real paymaster is someone else entirely, and agrees to confess all to Romana in exchange for amnesty.
Armed with Baano’s confession, Romana and Leela interrupt the summit just as it’s about to start from the beginning for the third time, and reveal that V’rell plans to assassinate Pule of Unvoss and frame Gallifrey. V’rell, aware that the delegates’ discussions are being broadcast live to all the temporal powers, reveals that a faction within the Monan Host has discovered destructive equations planted within their host system’s hyperspatial links by the Time Lords who “helped” restructure the links after the Dalek invasion. The Time Lords have the power to activate these equations whenever they wish, unravelling the entire planetary meta-structure.
V’rell believes that this revelation will shatter the trust between the Time Lords and the other temporal powers -- but K9-I reveals that he and his counterpart have disrupted the broadcast, and only the delegates immediately present at the summit know the truth. Upon learning this, Hossak pulls out the device she’s been using to wind Time backwards, and forces Romana, V’rell, and Leela out into the corridor, leaving the other delegates trapped in the debating chambers. Hossak knocks V’rell unconscious, announcing that she’s spent years of her life arranging this summit and is determined that nothing shall go wrong. Whenever something risked the destruction of all she’d worked for, she rolled Time back and started the summit over again.
The device Hossak is holding is only the trigger; the servitors themselves draw energy from low-level Time distortion, and generate the temporal energy necessary to roll back Time. Thus, the network itself is the source of the disruption, which is why it didn’t detect anything. But since K9-I is connected to the network, anything in close proximity to him was caught in an occlusion field and was not affected by the rollback; thus, since Leela was with K9-I the last time Hossak activated the device, she remembers the events of the previous iteration, and since K9-I was searching Flinkstab’s quarters before that, the holo-prints of Lexy’s death passed back through the temporal reversal. Hossak also reveals that she’s confessing to Romana because Romana will not survive the next rollback; by travelling to the planetoid after Time had rolled back, she’s travelled into her own past, and when Hossak rolls back Time to deal with V’rell before he can make his accusations against Gallifrey, Romana will cease to exist.
Hossak considers Romana’s death a small price to pay for the summit’s success -- but Romana then reveals the real reason that there are no heads of state attending these discussions. The real summit is taking place elsewhere, under Braxiatel’s supervision; Hossak’s summit is a sham, a public decoy to lure Free Time terrorists out of hiding. Stunned, Hossak vows to remove Romana from the timelines, thus creating chaos amongst the temporal powers so Hossak can save the day. Leela attacks Hossak, trying to stop her from activating the control trigger, but Hossak releases gas pellets embedded within her clothing and activates the trigger. Leela seizes the trigger and helps Romana to carry the unconscious V’rell back to the Presidential TARDIS. Even as K9 tries to access the defence shield’s codes so they can pass through, however, Time catches up with them... and rolls on past. The trigger is designed to focus and channel the time distortion generated by the servitors, but inside Romana’s TARDIS it is sealed in a separate dimension from the servitors. Time has stopped on the planetoid, but has not reversed, and Romana thus continues to exist.
Romana returns to the real summit and explains the situation. The delegates at the false summit are freed, and Hossak is placed under arrest. Romana releases a cover story claiming that Narvin went in undercover to flush out V’rell, but Narvin is enraged to learn that Romana, has informed the High Monan of the destructive equations -- and, in exchange for his silence, has given him instructions on how to remove them, since she never authorised their use in the first place. Narvin, irritated, reminds Romana that she and Braxiatel still have to prepare their case for the forthcoming judicial inquiry into the affair of the timonic fusion device.
Later, Romana speaks to Leela and assures her that, though nothing will happen to Flinkstab in public, his people are now unofficially investigating the death of the dancer on Coralee. Lexy remains alive, even though Hossak didn’t care one way or the other about her and only reversed Time so she could be seen as the person who brought peace to the temporal powers. Romana has also kept her word and allowed Baano to go free. All is resolved, but Leela remains upset, having seen so much death which has now never happened and has thus gone unavenged.