The whole story starts here as Gordon Shumway, a Melmacian who escaped his planet before it was destroyed, crash lands into the garage of the Tanner family. The Tanners call him "ALF" because he is an Alien Life Form and they decide to keep his presence a secret so that the U.S. Government will not take away the space being and subject him to experiments. From the beginning, there is no sanity for the Tanner family.
Everybody but Brian and ALF are leaving the house for the evening and Kate doesn't want ALF to babysit Brian, so Willie calls their ever-snooping Mrs. Ochmonek from the neighbor. ALF is told to stay in the bedroom, but when Mrs. Ochmonek starts to watch Psycho, which ALF wants to see, he can't resist sneaking out of the bedroom. Mrs. Ochmonek is in for some unusual experiences.
ALF bumps his head and loses his memory. All he knows is that his name is Wayne Schlagel and that he's an insurance agent. The Tanners try to make ALF remember who he really is - cue clips from earlier episodes.
ALF still believes that his name is Wayne Schlagel and that he's an insurance agent. Worse still, he has called the police to the Tanners. The Tanners have only a short while before the police arrive, so they try to make ALF remember who he really is by telling more stories from the past - cue more clips from earlier episodes.
ALF starts to go through a phase where his erratic behavior and hunger for cats will, in his own words, make him "ALF to the tenth power". He wants Willie to build a cage where he can be locked in until the phase is over. Will the cage be strong enough? Can they keep him locked in when he tries to plot himself out?
There's a power blackout, so ALF is passing the time by watching the Tanners' neighbors, the Ochmoneks, who are fighting. By dinner time, the power has come back so the Tanners can have dinner. Then comes another, short blackout. Trevor Ochmonek appears at the Tanners' door, seeking peace and quiet from the angry Raquel. Soon after, Raquel comes to demand that Trevor return home. The Tanners persuade him to do so. Night falls and ALF hears the Ochmoneks continue fighting. Suddenly it becomes silent. Too silent for ALF, who's convinced that something foul has happened at the Ochmoneks...
ALF thinks he's won in a publisher's sweepstakes, but the actual truth is that he subscribed to "hundreds of magazines" (Willie probably exaggerates here)... The next leaflet ALF gets his hands on *does* promise free gifts, but only if the family comes to listen a sales pitch for vacation homes. The Ochmoneks are going there, so Trevor invites the Tanners to come along. Turns out he is a pilot who flew in the Korean war, so they are able to fly instead of a seven-hour drive. The reluctant Willie eventually warms to the idea, but ALF has to stay home. Or is it that he should stay home?
After ALF watches "Crimestoppers" and sees a guy resembling Willie who is wanted for polygamy, he tries to hide Willie. When the FBI takes Willie in for question following an anonymous tip, everyone assumes that ALF called it in.