Tony (Ike Eisenmann) and Tia (Kim Richards) are other-worldly twins endowed with telekinesis. When their Uncle Bene drops them off in Los Angeles for an earthbound vacation, a display of their supernatural skill catches the eye of the nefarious Dr. Gannon (Christopher Lee) and his partner in crime, Letha (Bette Davis), who see rich possibilities in harnessing the children's gifts. They kidnap Tony, and Tia gives chase only to find Gannon is using her brother's powers against her.
After some violent confrontations with his new classmates, Daniel LaRusso learns karate from Japanese handyman Mr. Miyagi, in order to defend himself.
One of the US Air Force's most modern tactical aircrafts, an F-100 with a new laser guidance system, crashes into the sea near Malta - a region where the Soviet forces are highly present, too. The CIA immediately sends out their best secret agent, Ken Tani, to salvage the system before it falls into enemy hands. To ensure his loyalty, they bring his two young sons to a nearby hotel on the island.