Medusa, a planet from another solar system, drifts into Earth's system. The surface of this planet is no longer habitable and the inhabitants have moved to a high-tech underground city. The society is ruled by women, all of them beautiful. Men are considered mentally inferior and divided into two categories: the "adequately intelligent," who are selected by women to act as their personal "domestics" for household chores; and the remainder, who are forced to perform menial labor under the supervision of female guards. The guards are attired nicely in visored helmets, boots, hot pants, and elbow-length gloves which are used to control the men through some sort of apparent force. Two of the men from Medusa escape and head to Earth, determined to be free of their female oppressors, but they are pursued by two Medusan women. When the Earth authorities fail to help capture the fugitives, the Medusan women take two Earth scientists (a man and a woman) back to Medusa until an exchange can be arranged. The earthlings are forced to take their designated places in Medusan society. The man is chosen as a domestic, sometimes forced to work on a city maintenance crew, and the woman is assigned an elite white-collar job. The men and women from both worlds adjust to their new surroundings as the battle of the sexes continues.