While transporting delegates to a special Federation conference on Pacifica, the U.S.S. Enterprise picks up two representatives from the newly discovered planet of Antede III. Unaccustomed to space flight, the aliens arrive on the ship in a self-induced coma to deal with the trauma of their voyage.
En route to the conference, Picard and the crew are taken aback by the unexpected arrival of Lwaxana Troi, who also happens to be on her way to the meeting on Pacifica. Upon finding himself the object of Mrs. Troi's passions, Picard turns to Counselor Troi for advice. She explains that her mother is at "the phase," a mid-life period when a Betazoid woman's sex drive increases tenfold!
Reluctant to reject Mrs. Troi's amorous advances, Picard decides to seek refuge from her in the holodeck. As a result, she redirects her search for a mate to the other men on the U.S.S. Enterprise. Her "manhunt" ends on the Bridge when Mrs. Troi eyes Riker and announces to the crew that the two will soon be wed.
Meanwhile, when Dr. Pulaski reports that the Antedians are regaining consciousness, Riker enters the holodeck to inform Picard of the delegates' condition. He is followed by Lwaxana, who loses interest in both him and Picard after meeting Rex, the charming bartender in a Holodeck-created 1940s bar. To her chagrin, she later finds out that her dream man is only an illusion.
Returning to reality, Picard and Riker discover that the Antedians have fully awakened. They also learn, via Mrs. Troi's telepathic powers, that the Antedians are not delegates, but assassins sent to blow up the conference site using explosives hidden in the lining of their ceremonial robes.
While the Antedians are taken into protective custody, Picard thanks Mrs. Troi for saving the lives of the crew and assuring that the conference will proceed without incident. As Mrs. Troi prepares to beam down to Pacifica, she gives the captain one last playful reproach for his "lustful" thoughts as she dematerializes.