Tsar Nicholas II, the inept last monarch of Russia, insensitive to the needs of his people, is overthrown and exiled to Siberia with his family.

Two escaped convicts are found hiding in a rocket ship built by a renegade inventor, who forces them to become the crew for a trip to the Moon. Also on board, as inadvertent stowaways, are his assistant and his secretary; and none of them are aware that the inventor is actually a Lunarian explorer sent to Earth by the dying Lunar civilization.

The series follows the mystery-solving adventures of the Teen Angels—Brenda, Dee Dee and Taffy—and their friend Captain Caveman (or Cavey for short), a prehistoric caveman and superhero whom the girls discovered and thawed from a block of ice. The concept and general plot for the show was seen as a parody of "Charlie's Angels".