The second season begins with the gang coming across a crashed space shuttle where the service mechanoid, Kryten, is still attending to the officers, even though they have long since passed away. The crew take Kryten back aboard Red Dwarf where Rimmer puts him to work cleaning, cooking, ironing etc.
A mail pod arrives in space and Rimmer recieves the belated news that his father has passed away and is devastated, even though he hated him. To alleviate his sadness of the news (and the fact that he has a $8,500 tax bill), the crew try out a new Virtual Reality game where all your desires and fantasies can come true, but even Rimmer`s mind has its own way of stabbing him in the back.
After partying away to the anniversary of Rimmer`s death, Lister and Cat wake up with broken legs, Lister`s jigsaw has been completed, four pages have been torn from his diary, the clock is four days ahead and the black box is missing. The crew go after the black box and discover it in a shallow grave with a gravestone that reads `To the memory, of the memory of Lisa Yates`. Lister comments that he once dated a girl named Lisa Yates.
While going through Kochanski`s personal things, Lister finds a photograph of him and her getting married. Remembering something from the past, he reads Rimmer`s diary and finds a piece where Rimmer thought he saw his own head pop up through the table and say that he came from the future to save his life which Rimmer believed to be an hallucination.
Holly shows the first signs of his computer senility and endangers Lister`s life which activates the back up computer. The team rally around the new computer Queeg, but soon realise that he is a maniacal beast who demands order and proper ship regulations.
Holly claims to have invented a matter transport device called the "Holly Hop Drive" (A red box with a stop and start button on it) and the crew try and use it, but it doesn`t bring them to earth, it brings them to a parallel universe where women are the dominant sex. While Rimmer is trying to avoid his opposite`s sexual demands, Lister seems to be getting on very well with his. The Cat`s opposite (unfortunately for him) is a dog, and even Holly has an opposite, Hilly.