When the Cleaver brothers, Wally (Tony Dow) and Theodore "Beaver" (Jerry Mathers) saw an advertisement in the back of Robot Man of Mars comic book featuring a genuine Florida alligator for only $2.50, they sent away for one. But when a tiny baby alligator arrived instead of a full grown one as they had expected, the Cleaver boys were disappointed but still enchanted with their new pet.

For a time they hid the baby alligator in the toilet tank of their bedroom bathroom. But they soon realized they couldn't keep the alligator a secret from their parents and confessed their deed.

Wally and the Beaver eventually gave the growing gator to an alligator farm owned by Captain Jack (Edgar Buchanan) who had earlier given the boys advice on how to feed and care for their pet.

Consequently, in appreciation, of his kind efforts, the boys had named their gator Captain Jack. In a subsequent gesture of kindness, Jack (the human) told the boys that their pet would be well cared for and that they would be given lifetime visitation rights to see their pet at the alligator farm.