General Darnell and Lila Brown notice that Diana and Steve Trevor haven't come to work, and they go looking for them. They find Steve asleep and are unable to wake him. Diana has gone missing, but more investigation leads to them finding Etta Candy and Wonder Woman asleep at Holliday College. Like Steve, they will not wake up.
The story then shifts to a flashback to tell the story of how these three ended up in this state. Diana receives a message through her Earrings from Queen Desira of Eros on the planet Venus. She needs Diana's help and explains that, while sleeping, we all have an Astral Body that can travel great distances. Diana dresses as Wonder Woman and visits Etta Candy at Holiday College so that if she is found asleep no one will know her secret identity. Etta insists on coming along, so she goes to sleep as well. Desira insists that they bring someone with military experience, so they seek out Steve Trevor, who also joins them.
In Eros they learn that the people want to be sent to prison, begging Marya, their ruler, to sentence them for as long as possible. Marya explains that one woman in particular, Rebla, enjoyed her time in prison as it allowed her to play fun games and work on her electrical engineering projects, especially a paralyzing ray gun. Recognizing her talents, Marya sentenced her to freedom, making her the ruler of Trans Mountania depsite Rebla's protests.
Rebla didn't take well to leadership and wanted to spend time enjoying herself as she did in prison rather than fulfilling her responsibilities. This leads to Marya waging war against Rebla. However, Rebla outfits her all male army with paralysis guns, and they make quick work of Marya's all female army despite Wonder Woman's attempts to teach them how to use paralysis ray blocking bracelets that she invents.
Eventually the men capture all of the army including Etta, Steve, and Wonder Woman, whom they keep paralyzed so that she can't escape. Wonder Woman tricks Rebla, though, into also becoming a prisoner since she had enjoyed it so much in Eros. In Trans Mountania, however, the prisons are controlled by men, and they make prison a harsh and unpleasant place. A man, Dominus, takes over rulership of Trans Mountania and of Eros.
Steve Trevor manages to escape but can't free Wonder Woman from paralysis. He frees Rebla, who now sees the error of her ways. She frees Wonder Woman who stops Dominus from executing Etta and Marya just in time. Marya reclaims the throne of Eros and puts Rebla back in prison where she can work on her electrical studies.
Their work done, Wonder Woman, Steve, and Etta travel back to Earth and re-inhabit their bodies, which have been sleeping for ten days.