After their spaceship takes off with Jerry and Alice inside, Fi and Fum attempt to return them home but end up in the far future . While exploring, the kids are arrested for not having numbers and for exposing their faces in public.
The saucer lands in a time when all inhabitants on the planet are shrunken. And they distrust anyone who is bigger than them.
Fi and Jerry are arrested and accused of being "robot rustlers" when they come to the aid of bumbling robot Goro.
A mad scientist determined to create the first android rewires Fi and Fum, turning them into his slaves.
When the lost saucer crashes into the underwater city of Atlantis, ruler Nepto converts the saucer into a TV station and forces Fi and Fum to perform for the cameras.
The spaceship arrives in a land where a paranoid ruler has decided to protect his people by making everyone invisible.
When the saucer lands on 25th century Earth, they find that all power supplies have been depleted, so three rebel scientists attempt to use the Dorse to operate a treadmill generator.
When Fi and Fum return to their home planet with stray travelers Alice and Jerry in tow, Commander Stickler decrees that the androids must be recycled.
The space travelers land on their home planet in the future and discover people have reverted to the stone ages, and they find themselves terrorized by a half-chicken, half-elephant creature.
The Dorse brings a Chickaphant egg aboard the ship, and when it hatches, the crew is faced with a baby Elephicken.
The crew find themselves in a land where the laughing gas is pumped into the air and it's illegal not to smile. This is problematic for the androids, whom the gas has no effect on.
The crew find themselves in a land where exercise, working and being thin are against the law.
Fi and Fum are arrested and brought to court for a traffic violation, where they discover a narcissistic ruler has cloned an entire civilization in his own image.
Fum gets amnesia and falls in love with a beautiful android who mans a power plant.
The saucer breaks down in a land where people who don't have polka-dots on their faces are discriminated against.
When they stop to search for food, the crew find themselves in a land where the plants have developed the ability to speak.
