On stardate 41365.9, the Enterprise arrives at Starbase 74, in orbit above Tarsus III, for a routine maintenance check. Captain Picard and Commander Riker greet Starbase Commander Quinteros and a pair of small humanoid aliens known as Bynars whose species have become so interconnected with their computer technology that their language and thought patterns have become as near to that of a computer's as a biological lifeform's can.
Picard and Riker remain aboard as the crew disembarks for shore leave. The Bynars create a captivating Earth woman named Minuet using the ship's Holodeck.
Wesley, Geordi and Data investigate trouble in Engineering where the main computer indicates a catastrophic failure in less than five minutes, resulting in an immediate evacuation procedure. The Enterprise is remote-piloted out of the station where it is expected it will explode in open space. The crew learns that Riker and Picard are absent, and the ship does not explode, but instead warps away.
Unaware of what is going on outside the holodeck, Riker and Picard are lost in conversation with Minuet. Picard realizes that she is stalling him and exits the holodeck.
Picard attempts to contact the bridge, but there is no response. The computer explains the Enterprise is now heading for the planet Bynaus. Picard and Riker turn to Minuet for answers and she admits her part in the deception. The Bynars created her to keep them in the holodeck.
After arming the ship to self-destruct, Riker and Picard learn that the Bynars were stealing the ship to prevent a disaster on their own planet, and are able to help them. The Bynars express the gratitude of their people and request to be returned to the starbase to answer for their crimes. When Picard asks the Bynars why they didn't ask for help, the aliens reply, "You might have said no."
Riker returns to the holodeck, seeing a brunette sitting again at the bar, but realizes that it is not Minuet. He reports to Picard that Minuet is gone. Riker muses about the transient nature of love.