The Master has adopted the alias of Professor Thascalos (the Greek version of his name) and is using this cover to tap into the resources of the Newton Research Unit at Cambridge University to conduct time experiments. His TOMTIT (Transmission of Matter through Interstitial Time) experiment, assisted by Ruth Ingram and Stuart Hyde, is focused around transmitting matter by breaking it down into light waves. Having hypnotised Dr Percival, the Director of the Institute, into doing his bidding, the Master’s cover is maintained. He is particularly interested in examining a trident-shaped crystal in his possession, using it to attract a being he addresses with the words "Come, Kronos, come!"
The Doctor and Jo Grant visit the Institute following a hunch of his that the Master is back on Earth with his TARDIS. He finds time moving slowly as the TOMTIT experiments disrupt the normal flow while Hyde, who is caught in the field of the experiment, ages to more than eighty years. Brigadier Lethbridge-Stewart, who also witnessed the TOMTIT experiment, has the project evacuated and begins to hunt for the Master, whose cover has now been blown. The Doctor explains to Ruth and Jo that Kronos is a powerful Chronovore, a creature from outside time that feeds on time itself, who was once attracted from the vortex to ancient Atlantis using a crystal trident larger than the one used by the Master. That one remains in Atlantis. The Doctor suspects capturing the Chronovore is the Master’s aim too, forecasting such a step is a danger to the entire created universe.
Meanwhile the Atlantean High Priest of Kronos, Krasis, is transported through interstitial time by the Master and brought to Perceval’s office. The Master seizes the Seal of Kronos from the priest and uses it to control the Chronovore, invoking Kronos to materialise in the room. A white, feathered, male-like bird-like figure, Kronos exudes power and devours Percival without compunction. It is contained briefly by the Master, but breaks free and Krasis surmises this is because the Master only has the smaller fragment of the original crystal.
The Doctor and his allies have been alerted by the actions of the Master and he builds a time flow analogue to interrupt his rival’s experiments. The two enemies then spend time using time to trap each other, often with strange consequences: historical characters are transported into the present; Stuart Hyde is restored to youth, though Sergeant Benton is reverted to a baby when he is caught in TOMTIT’s flow; and several UNIT troops, led by the Brigadier, are frozen in a time bubble. The two Time Lords even pit their TARDISes against one another, and the Doctor is ejected into the vortex, but survives thanks to Jo and his TARDIS.
In ancient Atlantis the aged and wise King Dalios is troubled by the disappearance of Krasis and the threat to the true crystal of Kronos, which is guarded by the Minotaur at the heart of a maze. The Master has travelled to Atlantis in search of the true crystal and soon inveigles himself at the Atlantean court, wooing the vain and gullible Queen Galleia and embroiling her in plots and schemes. Dalios warns of the dangers of the time when Kronos served Atlantis, but his wife is not moved by his pleas or his suspicions of the Master, whom he knows not to be an emissary of the gods. When the Doctor and Jo arrive, the old King – far older than he looks, since Kronos gave him the power of longevity – forms a bond of trust with the Doctor and confides that when Atlantis turned from Kronos, their civilisation sought to end the link by which the Chronovore could be enslaved. But the crystal cannot be destroyed but only splintered. Dalios also tells the Doctor that the Minotaur was once his friend, but grew eager for the strength of a bull, and Kronos in blind sport gave this man his desire. The Doctor then faces the Minotaur to rescue Jo, duped into the maze by Krasis, and the creature is destroyed. The crystal is now produced from the maze – but the Master’s plotting with Galleia has borne fruit and he has usurped the throne, with Dalios deposed and arrested. Jo and the Doctor are soon detained too, and witness Dalios' sad death after mistreatment and torture.
When the Council of Atlantis meets, Galleia finds that Dalios is dead and, having loved and respected him, his end is enough to break her faith in the Master. Krasis, however, is still in his thrall and uses the great crystal to summon Kronos to Atlantis once more. The enraged Chronovore begins to destroy Atlantis and to survive the Master flees in his TARDIS, with Jo Grant in tow. The Doctor heads off in his TARDIS in pursuit while Kronos destroys the city and people of Atlantis.
The two TARDISes are now in the vortex, where the Doctor threatens their mutual assured destruction by causing a Time Ram by which both vehicles would occupy the same space/time co-ordinates. When he carries this threat out Kronos is set free and, thankful for this action, saves the Doctor and Jo and returns them to their TARDIS. On the Doctor’s insistence, the Master is spared too, but he flees in his own TARDIS before he can be apprehended. The Doctor and Jo return to the Institute as Ingram and Hyde operate the TOMTIT machine one last time, thereby returning the UNIT men to normality, albeit leaving Benton in a nappy. The machine then overloads, its time experiments at an end.