General Brigadier Jim McDivitt, a former astronaut, is interviewed on the TV show News Event on the subject of the rash of UFO sightings. McDivitt claims to have had his own close encounter during his Gemini flight, the eighth manned spaceflight. He was not able to obtain photographic evidence, but claims his close encounter was genuine. When he is asked whether he believes there is life on other worlds, he replies that he does. Afterwards, McDivitt signs autographs for Peter and Bobby.
That night, Bobby wakes up to a strange whistling noise. When he and Peter look out the window they see a strange red light in the sky. They believe they have seen a UFO. Next morning at breakfast they tell their siblings all about it, but they are rather skeptical. Greg comes down with a cut lip from shaving. Bobby and Peter tell him about the UFO and he says he read a newspaper report that it is mass hysteria. Peter and Bobby are adamant they saw a UFO and cannot wait to tell everyone at school.
Carol is taking a photograph of some fruit for a contest but is having trouble with the composition. Mike thinks the still life is too formal and staged, and when Jan and Cindy take some of the fruit for a snack, Carol decides to have a rethink. Then Bobby and Peter come home from school. They are down because everybody at school just laughed at their UFO story. They need some proof, so Mike suggests they ask Carol to take some photographs of it in case it shows up again. Carol agrees to let Bobby and Peter borrow her camera to take photographs.
That night, Bobby and Peter camp out in the backyard for their UFO watch. It takes some waiting, but the UFO shows up again. Peter and Bobby are ready with the camera and start snapping. But in fact Greg is creating the UFO with a flashlight, a sheet of plastic, and a whistle. Marcia comes in with a thermos Greg wants to borrow for his weekend fishing trip and realizes what he is up to. Greg says it is revenge for Bobby and Peter squealing about him getting home late on Saturday. Marcia thinks it is a dirty trick, but loves it because they squealed on her last week as well. They continue the UFO prank together, and Bobby and Peter continue to take photographs, anticipating they will become famous.
Bobby and Peter rush to their parents with the camera and urge Carol to develop the photographs immediately. Carol says it will have to wait until morning as it is so late. Mike orders Bobby and Peter to bed. There, Bobby has dreams of a UFO from Klaputus landing in the backyard and he meets two Kaplutians. After planting their flag, taking Earth samples (balls), and allowing Bobby to take photographs of them, the Kaplutians offer to take Bobby to their planet to show their people that life exists on other planets. Bobby accepts with alacrity, and wakes up saying "I'm going on a flying saucer."
Next morning Carol develops the photographs and they definitely show something that looks like a UFO. Peter and Bobby are all eager to phone the newspapers, but Carol tells them to wait until Mike sees them when he comes home from work. When Mike examines them, he is not sure what to make of them. He decides to bring in an expert and calls Carter Air Force Base. Instead, they get a policeman, Captain McCartney. McCartney says the Air Force referred the matter to them as they refuse to investigate UFOs because they do not believe in them - and neither does he. He has come to this conclusion after years of UFO reports at the police station. He examines the photographs and remains unconvinced.
Then Greg and Marcia come home, where they find Captain McCartney has been called in over the UFO photographs. Realizing their prank has backfired, they bring Mike to the attic, where Greg shows him how the UFO works. But as they do so, McCartney hears the whistling noise. When he investigates, he sees the UFO for himself. Everyone else (except Marcia) rushes out to see it as well. All of a sudden, McCartney is a believer. He goes to the phone to report the incident. Marcia tries to stop him but fails, and McCartney reports the sighting to the sergeant. He orders the sergeant to alert the Airforce Defense Command, but it sounds like McCartney is being greeted with skepticism himself. He remains insistent and even has Peter take photos of him on the phone reporting the incident.
Upstairs, Mike orders Greg to come down and explain the whole thing to everyone. When McCartney sees how the UFO works, he is furious and returns to his old skepticism. But he agrees to keep Greg's UFO quiet if Greg does not tell anyone about his phoning the sergeant.
Greg's prank is prevented from snowballing beyond control, but he is still in disgrace. Peter and Bobby are very down on Greg and he has to think of ways of making it up to them. Mike and Carol forbid him to use the car during the weekend, which upsets his plans for the fishing trip. Greg demands to know how he can make the fishing trip without a car. Carol says he will just have to hitch a ride on a UFO.