Fang Rock is a small, rocky island in the English Channel. Upon it stands a lighthouse: from the lamp room, Vince spots a shooting star which appears to land somewhere in the sea nearby. As first a strange fog engulfs the island and then the electrical supply for the light begins to act erractically, the lighthouse keepers are faced with an increasing threat. Ben, the headkeeper is adamant that electricity is the future; Reuben, believes that oil is better and, given the current situation, more reliable. Ben's attempts to sort out the erratic electricity supply appear to lead to his death. The arrival of two people, the Doctor and Leela, apparently lost in the fog, their ship beached on another part of the island brings some comfort to Vince but arouses the suspicions of Reuben. When Ben's body disappears, it supports the old tales of Fang Rock, about the Beast - which caused the deaths of two lighthousekeepers and the madness that gripped the third.

Despite help from the Doctor, the light cannot be restored and so a ship founders on Fang Rock. The survivors are two financiers on their way back to London from the continent - Lord Palmerdale and Skinsale, Adelaide - Palmerdale's secretary, and Harker - the sole surving member of the ship's crew. As the night progresses the Doctor tries to impress upon them all that they are under seige: that the fog was generated to isolate them and that their enemy is capable of manipulating electricity...

A shuttle carrying the relief crew to the refuelling base on Titan is passing through a field of asteroids. En route they also encounter a strange phenomenon. Everything appears to be all right so they continue on to Titan. When they arrive, the crew of the shuttle make their way to the mess area where the old crew are celebrating the end of their tour of duty. To the horror of the old crew, the relief team pull guns on them and shoot them dead. Lowe, the base supervisor tries to contact the relief crew so that they can report in. When he checks the mess area on the monitor and sees the bodies and then tries to speak to the head of the relief crew, Safran, Lowe realises that something has happened to the relief crew. He transmits a distress signal and then finds a place to hide before the infected relief crew can get to him.

The TARDIS picks up the distress call. As the Doctor sets course for Titan, Leela senses that something is wrong. Another message comes through rescinding the distress call: everything is under control. Again, Leela senses that something is wrong and that the sender of the second message was not human. The TARDIS passes through a strange phenomenon. As the Doctor checks the TARDIS instruments, there is a discharge between the console and him and he falls to the ground. A similar discharge has no effect on Leela though. The relief crew on Titan await the Doctor's arrival but also know that they must eliminate Leela as she has been rejected...

Colby is debating about a recently discovered skull which was buried in lava that dates back 12 million years: the skull comes from a species of man previously not known to exist until 8 million years later! Dr Fendelman is making use of a new device, a time scanner which should allow them to look back into the past. Sitting in another room, as Thea watches, the skull seems to glow. A hiker, out in the nearby forest finds himself being pursued by something. He begins to slow down and finally comes to a stop, as if unable to move his legs. His pursuer then attacks. the following morning, Colby is out walking a dog when the dog finds the hiker's body - a look of terror on the face of the corpse. Fendelman is concerned that bringing the police in will delay the experiments - perhaps if the body was found elsewhere? Thea is not happy about this deception, then when a private security team arrives, effectively trapping them in the lab - it looks as if Fendelman will stop at nothing to complete his research.

The TARDIS is also affected by the time scan and is nearly plunged into a hole in time. Tracing the scan the Doctor is horrified to learn that the source is on Earth: the planet could be destroyed if the scanner is not shut down. Encountering a villager, Ted Moss, the Doctor asks him about ghosts and strangers. Moss evades the question about ghosts but confirms that there are some scientists working at the nearby Priory. Finding the Priory guarded though, the Doctor and Leela search for another way to get in.

Citzen Cordo waits for news about his father's death. On learning that his father has died peacefully, Cordo is then dispatched to the Gatherer to pay the death taxes. Unfortunately, Cordo does not have enough money - the taxes have increased. The Gatherer reminds Cordo that it is every citizen's duty to be aware of the changes in taxes. He will have to pay the deficit - by working extra hours and not sleep until the debt is paid. Cordo concludes that he will be unable to pay and so goes to the rooftop to throw himself off.

The Doctor and Leela arrive on Pluto, but far from a lifeless rock they find that it has been terraformed. They also spot Cordo and save him from killing himself. A siren alerts them to the fact that citizens are not allowed to look at the suns. Rather than being sent to the correction centre, Cordo concludes that his only other option is to find and join the Others, outlaws reputedly living in the undercity. The Others don't accept new recruits gladly, but are willing to let the Doctor try and obtain some money for them - with Leela as hostage.

The TARDIS has reached the edge of the universe: new stars and new planets will form there in time as the universe continues to expand. For now, though, there is nothing - except for a spaceship within the vicinity. Avoiding a newly forming nebula, the Doctor materialises the TARDIS inside the nearby spaceship. The crew: Jackson, Herrick, Orfe and Tala come from the planet Minyos and are searching for the last hope of their race - the P7E. Unfortunately, their ship is damaged and they are now being drawn into the nebula. The Doctor helps make a temporary repair, long enough for the Minyans to re-discover the signal from the P7E. The signal is coming from the nebula - so now they are heading back into the danger!

After some talks with the Vardans, the Doctor returns to the TARDIS. Keeping Leela excluded from his plans, the Doctor sets course for his home planet - Gallifrey. Upon arrival, he declares himself as candidate for the presidency. As there are no other candidate it would appear that he will, by default, become President of the Time Lords! As everything is prepared for his inauguration, the Doctor makes various demands. His behaviour seems more erratic than usual and Leela finds herself being banished to outside the Capitol! Could it be that the Doctor intends to betray his own people and allow Gallifrey to be invaded by the Vardans?