On stardate 41636.9, the USS Enterprise goes to Angel One, a reclusive world whose inhabitants have a constitutional oligarchy dominated by women and males are treated as a lesser social class. The females of the planet are like Amazonsâtaller and physically stronger than the males. Females occupy all positions of authority, run the government and control the planet's technology, while the males of Angel One are the "weaker sex", filling subservient roles as secretaries, servants, and househusbands.
The crew arrives to locate possible survivors from the freighter Odin which has been missing for years. Captain Picard has Counselor Deanna Troi do the honors of greeting Beata, the planet's leader, to explain their presence. Deanna heads up an away team with Commander Riker, Lt. Commander Data and Lt. Yar, and beams down directly to Beata's office. Beata refuses to answer any questions stating the Federation has to petition her council. Deanna opens the petition saying if any survivors are found, they will be removed from the planet and the Enterprise will leave. Beata says the council will adjourn to announce a decision later.
In space, the Enterprise receives a distress call from a border outpost near the Romulan Neutral Zone. Several Romulan ships have penetrated the zone and Starfleet wants the Enterprise there in case something happens. Picard walks with Lt. Worf, giving orders as they pass a holodeck. Suddenly, Picard is struck in the chest by a snowball. He turns in annoyance to see young Wesley Crusher exiting the holodeck with a friend. The two boys explain they were having a ski lesson and apologize for the horse play. Worf and Picard then take notice of a sweet fragrance in the air, which Worf describes as "stimulating", but Picard dismisses it.
Back on the planet, the away team is summoned back to council chambers. There, Beata explains that there are four survivors from the Odin, all males, but says they may be hard to find since they are considered fugitives, and their presence has caused a disruption in the "natural order" of their ways. Data believes he can locate their position by scanning for the presence of material that may have been aboard the Odin, but not native to Angel One. Such a material would show up like a beacon and lead them to their location.
Back on the Enterprise, Wesley lies in sickbay with a loud cough and fever while his mother, Dr. Crusher, looks over him. She guesses he picked something up from his class field trip to Quazulu VIII, but Wesley assumes the transporter bio-filters should have screened any infections. Beverly mentions that if the virus is unknown, the filters wouldn't have screened it out. She notifies Picard to have all the students placed in isolation, but Picard himself begins to fall ill.
Back on the planet, Data accesses the Angel One library computer and discovers the element platinum is not naturally occurring on the world. He requests the Enterprise conduct a scan for it. At the same time, Picard is now in sickbay himself and feeling miserable and has temporarily put Geordi La Forge in charge of the ship. On the bridge, Worf locates a trace of platinum on the surface and La Forge relays the coordinates to the away team. Riker informs Beata of the trace and she allows the away team to conduct their search; however, she curiously requests for Riker to remain behind. Riker, confident that his people can handle things without him, indulges in Beata's company.
Meanwhile, the other three beam to a secluded encampment where they find a man sitting calmly in a folding chair. The man identifies himself as Ramsey, the "ad hoc" leader of the Odin village. He admits he knew they'd be found eventually when Data explains about the platinum being traced to a pin on Ramsey's flight jacket. Deanna explains the urgency that the Odin survivors come to the Enterprise immediately, but Ramsey says he and his men aren't leaving. They have been on Angel One for seven years and during that time have taken wives and started families. Deanna indicates Beata's desire for them to leave, but Ramsey becomes angry, exclaiming her wishes are not his commands and neither are they the Federation's. Data says he is afraid that Ramsey is correct. The Odin's crew are private citizens, their presence is not considered a violation of the Prime Directive and the Federation cannot force them to leave.
Back in Beata's quarters, Riker has dressed in the thin, revealing tunic, typical of the males of the world. With lights dimmed to a romantic level, he sits with Beata who lays provocatively on a couch. Riker asks why she hesitated to divulge the existence of the survivors. Beata says Ramsey and his men are anarchists, obsessed with spreading lies and encouraging dissent among her people. Ramsey believes men should enjoy life, while the women struggle with the drudgery of it. Riker explains that Ramsey is from a society where men and women share in life equally and delight in their sexual differences. Beata says she doesn't feel men are inferior; however, the women of her world took charge when men showed a natural tendency for hostility and warfare. At Ramsey's camp, the away team beams back to Riker's location, and once the coast is clear, a woman emerges from the shadows. It is Ariel, one of Beata's associates, and she quickly embraces Ramsey. Back in Beata's quarters, the away team explains Ramsey has refused to leave. Beata becomes furious and says she has no choice but to sentence Ramsey and his men to death.
Back on the ship, Picard lies in his bed with a high fever. As Beverly gives him some soup she catches a whiff of the strange, sweet fragrance. Picard mumbles that he smelled something similar when he ran into her son. Beverly quickly realizes that this is how the virus travels - an airborne microbe whose sweet scent inspires deep inhalation and once inside the body, it becomes a virus. She rushes out of the room with work to do.
On the planet, the away team prepares to depart when Beata unexpectedly summons them. They return to the council as guards lead Ramsey and his men into the room. Among them is Ariel. Ramsey is furious, believing the away team has turned them in, but Beata tells Ramsey he and his traitorous partner Ariel have only themselves to blame. She knew Ariel had been sneaking off to meet with her fugitive husband and tomorrow they will both die together. Riker protests, asking Beata to stay the execution if he can convince Ramsey and his people to leave. She agrees, allowing Riker one more chance to change Ramsey's mind. In a holding cell, Riker tries once again to convince Ramsey to leave, but he remains adamant on staying, even if he is executed for it. Riker states he'd rather face a court martial than watch innocent people die and contacts the Enterprise to have everyone beamed up. He is surprised when Dr. Crusher answers the call and is apparently now running the ship. She refuses to take the risk of anyone beaming aboard since the virus is out of control. Riker orders Data, who won't be affected by the virus, to return to the ship alone and get to the Neutral Zone before it's too late.
After spending a night stranded on the planet, the team awakens the next morning and are offered to witness the "reaffirmation of Angel One's moral imperative". Riker declines, but then Data calls for him. Riker is angry, wondering why Data hasn't left yet, but Data indicates the order stated "get there before it's too late". Data calculates a 47 minute window to reach the outpost before the Romulans do and Deanna thinks it's 47 minutes that they can use to save Ramsey.
They head to the council chamber where the prisoners are ready to face death. Beata demonstrates their manner of execution, a disintegration platform where Beata's servant, Trent, phases a vase out of existence. Beata has Ramsey placed in the booth to die first. Riker tries again to sway Beata's decision explaining that Ramsey and his followers are symbols of change, and killing them will only make them martyrs. It will accelerate, rather than stop, the coming movement of equality between the sexes of Angel One. Trent readies to activate the disintegrator and Ariel shouts for mercy. Beata stands down and calls another council meeting.
Back on the ship, Dr. Crusher calls Data to announce she found an inoculant for the virus. Data sees they still have a 17 minute window and calls down to Riker who instructs Data to beam everyone up from the holding cell in 10 minutes. In the meantime, the council reconvenes, and Beata announces that Ramsey and his followers will not be executed. Instead, they will be exiled to a remote location on Angel One, to promote their heresy as they wish. Anyone who wants to go with them will be allowed. This solution won't stop the inevitable decay of Angel One's cherished system, but at least it will slow it long enough so that Beata won't have to be around to see the damage. With the matter resolved, Riker signals for the away team to beam up. Returning to the ship, Riker takes command and heads to the Neutral Zone.