After an indulgent night at a Voxnic bar, the Doctor awakens with a dreadful hangover, having dreamt of a female Voice which warned him of a danger to the structure of Time. Peri chastises him about his drinking and tells him that the TARDIS has materialized early, next to a huge spaceship, and that the console is making strange noises. The Doctor soon determines that the TARDIS is detecting Time spillage from aboard the spaceship; someone is illegally experimenting with Time travel, and the Doctor has no choice but to investigate.

The ship's computer has begun behaving strangely; she starts to hiccough when talking to Grant and claims that she's started hearing voices. Captain Slarn is demanding to see Grant, who reluctantly goes to Slarn's quarters with no good news to pass on. Slarn's steward has confined him to a lava bath, as the captain has a tendency to become ill when things don't go his way -- and as Grant well knows, once the captain has passed his psychosomatically created illnesses on to the rest of the crew, he immediately becomes better.

As the Doctor and Peri flee from the monster, the Doctor tries to lift Peri's spirits by telling her about an actor named Rudolf Musk, who was once in a similar situation. His stilted performance as he was swallowed whole so irritated the creature eating him that it regurgitated him, saving his life. Peri is unimpressed for some reason.

Grant eventually finds his way out of the clouds of steam coming from Slarn's lava bath, to find the Captain very unwell indeed. Slarn needs to be cossetted and reassured that all is under control, and he warns Grant that unless the intruder is found and killed then Slarn's illness will spread to infect the entire ship. The computer interrupts with news of a second intruder -- a young Earth female who seems to have appeared from nowhere. Slarn lasciviously orders Grant to bring her to him for "interrogation".

The Doctor and Peri, nearly out of breath, are saved at the last minute when a bulkhead slams shut between them and the monster. The computer contacts them and apologizes for the shock -- but the Doctor is more concerned with the fact that they passed a dozen perfectly serviceable bulkheads on the way here. They were brought to this spot deliberately, and perhaps even the Time experiments they first detected were a lure to get the Doctor on board. He begins trying to open a nearby door, and informs Peri that the creature which chased them was a Maston -- one of a species which became extinct over a million years ago...

What nobody yet knows is that the computer is under the total control of the Voice which spoke to the Doctor in his dream. The Voice has lured the Doctor to the ship to drain his knowledge about Time travel and aid her experiments while Slarn is distracted, indulging himself with Peri. Grant contacts the computer, asking her to divert the search parties so he can arrest Peri in person and improve his standing with the captain. The Voice, realizing that Grant will first question Peri and learn about the Doctor's presence, orders the computer to deal with the problem.

The computer refuses to let the Doctor go, advising him that the chances of Peri having made a soft landing are in the region of eight million and three to one against. Nevertheless, she has indeed landed safely on top of a man named Snatch, whose partner Seedle becomes extremely suspicious when Peri offers to have her friend the Doctor check whether Snatch is all right. Peri finds herself accused of aiding and abetting malpractice, and before setting off to question the Doctor, Seedle and Snatch attach a clip to Peri's jacket to screen her from the ship's electronic sensors. They refuse to tell her who they are or what they were doing in the ducting in the first place.

Slarn's steward massages his tension away as Slarn sulks, whining that people don't like him, and wondering why Grant isn't as fat as him. The steward soothes and reassures him, claiming that Slarn is far too busy with his responsibilities to spend time in the gymnasium as Grant does. Slarn contacts the computer and demands to know why it's taking so long for the Earthwoman to arrive, and despite the steward's ministrations Slarn's impatience continues to grow...

Grant contacts the computer, but doesn't pay close enough attention to her attempts to imply that something is seriously wrong with her. He's only concerned with finding the Earthwoman, and although she has now disappeared from the ship's sensors, he demands to be given her last known location so he can look for her himself. The Voice, angry with the computer for failing to kill Peri, orders her to give Grant the information he wants -- once he finds Peri the Maston can kill them both.

Grant destroys Barton, who collapses to the floor and gradually shuts down. The Voice orders the computer to deactivate its conditioning and let the Doctor's curiosity lead him into the trap. Meanwhile, Grant frisks the Doctor and is surprised not to find a gun. He'd assumed the Doctor was working for the police, who frequently use devices to confuse surveillance monitors. But the Doctor isn't carrying one; so why didn't the computer report his presence? Grant admits that he's been stealing art treasures from the planets this ship has visited, but can't imagine who on board would be involved in the Time experiments which the Doctor describes; the only scientists on board are social scientists conducting a census of the galaxy. Barton manages to tell the Doctor that the computer had ordered it to take him to a secret compartment on the level below, and the Doctor and Grant set off to investigate.

Seedle and Snatch question Peri further, convinced that they've stumbled onto a den of iniquity which will result in their promotion once they've solved this case. They still deny that they're policemen, however, and claim rather implausibly to be environment inspectors. They do admit that they're investigating the theft of art treasures and know that Grant is involved; they haven't approached the captain in case he too is involved in the thefts. They eventually stumble across Barton, whose last garbled attempt to describe the fight which destroyed him manages to convince Seedle and Snatch that Grant, and the mysterious "Doctor" Peri describes, are one and the same man...

The Voice withdraws slightly, disappointed by the Doctor's weakness. She explains that she has studied the information the census ship has gathered, on all of the civilisations of the galaxy, and has become shocked by the prevalence of war, death and cruelty throughout even great cultures' history. Now she has a plan to change all that...

Seedle and Snatch locate Grant, sneak up on him, overpower him and take his gun away. Snatch then beats a confession out of him, but Seedle then demands that he confess to being Peri's friend the Doctor as well and ignores both Grant's and Peri's attempts to deny this. Eventually Peri manages to describe the Doctor and Grant manages to explain that he's behind the door in the wall.

Slarn is all ready to "interrogate" the Earth female, but there's still no sign of her... and when he contacts the computer she informs him that both the Earthwoman and Grant have vanished. Together. Slarn, furious, feels his rage grow despite his steward's attempts to mollify him. To his steward's horror, Slarn decides that he's incubating *mors immedicabilis*, the incurable death -- which will kill every living thing on board if it escapes quarantine...

The Doctor realizes that Voice has no intention of warning the crew of the danger, and it informs him that if he tries to escape back to the TARDIS he may find the Maston still roaming the ducting; the computer had originally brought it here to distract the crew while the drones constructed this compartment. Voice claims that since the creature is only obeying its primitive instincts, and since the crew will die due to Slarn's actions, her own metaphorical hands are clean, and departs angrily when the Doctor scoffs at her rationalisations. Seedle manages to open the door, convinced Grant was guarding a safe containing the stolen art treasures. The Doctor warns him and the others of the danger they now face; they must get back to the TARDIS immediately.

Slarn studies the rapid development of his disease, fascinated, and ignores his steward's pleas for him to stop. He's never seen any of his illnesses develop quite so quickly before and doesn't even stop when his steward becomes infected. Much too late, Slarn realizes that he's even managed to infect himself...

As the Doctor and his companions near the TARDIS, they encounter the Maston again. Snatch tries to shoot it, but his gun is ineffective and the creature catches and devours him. Seedle, blaming himself, stays behind to hold off the creature while the others escape, and as they reach the TARDIS they hear Seedle dying in the distance. Meanwhile, the computer's Persona questions her inner Voice and learns that she picked up symptoms of the Doctor's intoxication when Voice contacted him in the TARDIS, explaining why the Persona has been acting so strangely ever since. Persona realizes that the Doctor was right; Voice provoked Slarn's illness and set the carnivorous Maston free in the ducting. Her claims to despise violence are fraudulent; she's a hypocrite whose only interest is in her own personal power.