The basic premise for the series, akin to the much later live-action sci-fi series Sliders, was the story of a band of adventurous, cuddly, dog-like creatures called Fluppies who use a crystal key to open inter-dimensional doorways. They are on a mountain of one world in perilous weather, and use the crystal key to escape, ending up in a supermarket on Earth.
Mistaken for regular dogs, they are captured and placed in a pound. As their only means of escape, Stanley, the leader of the Fluppies, manages to get a woman to pick him as a pet for her son, Jamie, with plans of returning to the pound to free the others. Jamie is disappointed at this new dog, which is smaller than he hoped, but takes him for a walk. Taking the opportunity, Stanley escapes his leash and makes a break for it, but Jamie pursues him so as to not anger his mother for losing the new pet so soon. Unfortunately, the chase leads to a construction site and Jamie finds himself in danger, forcing Stanley to reveal his intelligence and humanoid nature to save him. Meanwhile, Wagstaff, a rich collector of exotic animals, recognizes the Fluppies and vows to capture them.
Now with a secret, Stanley explains the situation and Jamie offers to help. Unfortunately, the boy only has enough money to purchase one of Stanley's compatriots, Tippi, and his mother won't let him keep her. Fortunately, Jaimie's neighbour Claire eagerly agrees to take her in. That night, as Jamie and Stanley sleep, the boy reflexively scratches the Fluppy's head, which causes their bed to fly. Once they awaken and learn how to control the flying effect, Stanley resolves to break his compatriots out that night and pick up Tippi to do so, inadvertently revealing their nature to Claire in the process. At the pound, Stanley and Tippi manage to free their friends and barely avoid Wagstaff, who had the pound opened to seize them.
The next day, the Fluppies depart to find another dimensional portal, but they need Jamie's help. He leaves school to aid them. This portal turns out to lead to a water world, and the company are flooded out and have to return to Jamie's home to dry out. Hiding in the basement, the Fluppies discover another portal inside that very house, but opening it releases a large rambunctious creature that runs about, throwing Jamie's home into a shambles before they can bring it under control. Although the gang manages to put the house in order before Jamie's mother comes home from work, she gets news that Jamie cut school. Angry at her son for playing hooky, she asks a lot of questions, which Jamie concocts a long story whilst the Fluppies clandestinely keep the alien creature pacified in the basement by feeding it flowers.
Hoping to avoid ruining Jamie's life any more, some of the Fluppies continue their search on their own while Stanley and Tippi keep the alien creature hidden in the basement. The venturing Fluppies come to a library and finally locate the portal to their home world. Unfortunately, while they are returning to tell the other Fluppies the great news, Wagstaff captures Ozzie, forcing Stanley and Tippi to ask for Claire's help. Jamie sees them depart in Claire's car as he and the youngest Fluppies ride on the creature in pursuit. Unfortunately, Wagstaff was expecting this and manages to capture Stanley and Tippi in his home and threatens to call the police on the children for breaking and entering.
With a desperate plan, the Fluppies convince Wagstaff to let the children "say goodbye" and signals them to scratch on all their heads. The combined strength of this magic tears the entire section of Wagstaff's house into the air. As the occupants struggle to keep their footing with the violent jostling, the Fluppies reach the portal at the front of the library and they crash land the building in front of it. As they struggle to open this portal, which enters into the Fluppies' home dimension, Wagstaff and his butler find themselves knocked inside by the creature while Stanley's company bolts to safety. Before Wagstaff and his butler can exit, the door closes permanently, leaving Jamie and Claire alone in their own reality.
Months later in winter, Jamie and Claire have grown to be close friends after this extraordinary adventure, but they miss the Fluppies dearly. However, Stanley suddenly appears, saying that adventure is an important part of life. His fellow Fluppies appear saying they missed Claire and Jamie, and Stanley reveals that he has found a way to stabilize the portal between his homeworld and Earth. Hundreds of Fluppies line up to pass through the portal, eager to tour Earth.