When Pugsley launches missiles from his bedroom window, they are mistaken for unidentified alien aircraft. Mr. Hinckley and Mr. Gilbert, investigators from the MSO (Mysterious Space Objects) Headquarters, go to the Cemetery Ridge district to investigate. They come across The Addams Family on a moonlight picnic and snail hunt. While Gomez and Morticia are Moonbathing, Lurch and Cousin Itt are cooking lunch and "talking" politics. The investigators think that they are aliens. The Addams Family hear radio reports of UFOs and think the investigators are aliens. The two 'aliens' seem shocked, so Gomez and Morticia lock them up for their own protection. Gomez gives them Pugsley's disintegrator gun to play with while he and Morticia pretend to feed Cleopatra so they can talk privately, but then Gomez realizes what he's done and takes the gun with him. When Kitty Kat frightens them, they try to escape, but are locked up in the stockade and iron maiden in the Play Room. Gomez calls the MSO for advice and reaches Professor Altshuler. Professor Altshuler thinks Martians have invaded and rushes over to see what the Addams Family has found.
- Professor Altshuler gets an eyeful of Cousin Farouk and Pierre.
- When Thing hangs up the telephone for Professor Altshuler, and when he hands Morticia the mail, he is a left hand instead of his usual right.
- Old Senator Addams, Cousin Galileo, Cousin Grope, Old Blood and Thunder Addams, and Old Cannonball Addams are mentioned.
- Despite Blossom Rock, Lisa Loring and Ken Weatherwax being credited, they only appear in the opening and closing credits.