Stardate 5710.5: The Enterprise receives a distress message from the planet Scalos. The planet is highly developed but the population is totally absent with no trace of bodies, death, or disease. Kirk beams down with a landing party to the transmission point of the distress message but they find no one. McCoy and the others run analysis while Kirk notices the buzzing of insect life even though the doctor says it doesn't show up on the scans. As Spock reports, a technician, Compton, takes water samples. McCoy looks at Compton and he disappears without a trace.
Kirk returns to the ship to investigate further and the crew is plagued by minor malfunctions. The captain then reviews the distress tape which shows a small group of Scalosians who report that there are only 5 survivors out of 9,000. The controls continue to malfunction and McCoy calls Kirk down for a checkup of all the landing party members. As McCoy examines him, Kirk hears the same buzzing noise and feels something touch him. When McCoy assures him he's not hallucinating, Kirk concludes they beamed someone aboard that is invading the ship. Communications partially goes down and Spock picks up a disturbance in Life Support. Kirk goes there with Spock but they're bounced back by a forcefield. It turns out only the security guards are thrown back by the forcefield. Kirk and Spock enter the chamber and find an alien device hooked up. When Spock tries to disconnect it, they're thrown back. When they try to blast it, their phasers disappear and they're shoved back by some invisible force.
Back on the bridge the computer recommends negotiation but Kirk refuses and plans to have the invaders take the next step. Kirk grabs a cup of coffee and sits down, but hears the buzzing noise. He drinks the coffee, unaware that something has been poured in it by the invisible invader. As Kirk looks on, the crew begins to slow down in his perceptions until they are frozen like statues. A woman appears on the bridge, one of the Scalosians from the distress message. When Kirk demands answers, she kisses him and introduces herself as the enemy.
The woman, Deela, explains that Kirk has been accelerated to the point where he is moving fast enough to be invisible to everyone else. She's clearly interested in him and not afraid to admit it and kisses him again. She says she's the Scalosians' queen and Kirk will be their king. He doesn't believe her and tries to stun her, but the beam is in regular time and she easily dodges it. She demonstrates her own accelerated weapon and disarms him. He tries to negotiate but she asserts that he'll eventually accept the situation. Kirk storms off the bridge to life support and Deela warns the other Scalosians he's on his way, but to be gentle with him.
Back in normal time, the crew notice that Kirk has disappeared. The captain gets back to life support where Compton meets him and tells him he can't enter, and he's under no orders. Compton is armed with a Scalosian weapon but Kirk disarms him only to enter and be stunned by the Scalosian leader, Rael. Compton comes to his aid only for Rael to knock him down. They discuss the cell damage done to Compton and Rael promises the remaining female Scalosian that they'll find another male for her.
Deela wakes up Kirk and explains that he can go anywhere he wants. Kirk tries to disconnect the Scalosian device but it's extremely cold and his hands are almost frozen to it. Kirk sees Compton, who is now dead of old age. Rael explains that Kirk damaged Compton's cells in the struggle, and the newly accelerated are sensitive to such damage. Kirk storms out and Deela complains to Rael about lying to Kirk that he was responsible for Compton's damage. It's clear that Rael is jealous of Deela's attentions toward Kirk.
In the medical lab, Kirk records a message to the others present and Deela arrives and lets him go ahead. Kirk explains everything and concludes that the Scalosians are prepared to put everyone on the ship into cryonic suspension. Deela then explains that their country was almost destroyed by volcanic eruptions, the water was polluted, and the radiation released hyper-accelerated them and rendered the males sterile. They plan to take Kirk and maybe one or two other crew down to the planet for breeding. He tries to convince Deela to let the Federation help them but she insists they are trapped jut as he is.
Rael calls Deela to the transporter room and while she's occupied, Kirk puts his recording tape in with the ones Spock is using, then sneaks off to the transporter room. Deela finds him there and tries to beam him down, but it doesn't work. She reports to Rael that it is malfunctioning even though it's clear she knows Kirk did something.
Back in real time, Spock hears the same buzzing noise and figures out what it is. He goes to the bridge to check things out.
Kirk and Deela go to the captain's quarters and they kiss, as he tries to grab her stunner. She appreciates the effort and the kiss.
Spock reviews the tape and then accelerates the playback until the image fades into invisibility and the sound becomes a meaningless buzz. In sickbay, McCoy finds Kirk's tape with the same buzzing noise recorded. Spock plays it back at a decelerated rate and they listen to Kirk's warning and Spock concludes they must match the Scalosians on their level.
Rael partially finishes repairs on the transporter and calls Deela, who doesn't respond. In Kirk's quarters, they embrace as Rael comes in and attacks the captain. Kirk manages to hold him off without taking cell damage until Deela can stun him. Deela defends her choice of males despite Rael's jealousy and orders him back to finish the repairs. Kirk has calmed down and seemingly has accepted the entire situation. Deela is rather disappointed at his sudden acceptance of the situation and notifies Rael of the situation.
McCoy has come up with a cure for the effects of the Scalosian water and Spock drinks the water so he can get the antidote to the captain. Kirk and Deela go to the transporter room but he takes her weapon and heads back to life support. En route he meets Spock and they stun Rael and then destroy the refrigeration unit. Deela arrives and comforts Rael, then wonders what they'll do with the Scalosians. She figures they'll quarantine the area and leave them to die. Instead they beam her down to the planet although she still believes they can't return to normal time. After they beam her and Rael down, Kirk takes the antidote and is restored to normal time and heads for the bridge. Spock completes the repairs to the ship at hyper-accelerated level then return to normal time using the antidote. The decelerated distress tape plays on screen and Kirk says goodbye to Deela's image as they leave orbit.