Basil the dog and Elvis the cat are always fighting. Lucy begs them to stop, but they won't. But Elvis the cat has had enough, so one night he sneaks out the cat-flap and doesn't come back.
Lucy is very upset. She makes posters and puts them all over town. But Basil misses Elvis and goes out to look for him. The alley cats help, and finally Basil brings Elvis home, to Lucy's great delight. This time, they don't fight, but curl up together and go to sleep.