On the way to Starbase 10, the U.S.S. Enterprise stops to deliver supplies to the 6 colonists of Gamma Hydra IV. A landing party consisting of Kirk, Spock, McCoy, Scott, Galway and Chekov beams to the planet's surface and finds that accelerated aging has taken place, killing most of the colonists. The only two survivors, an elderly couple who claim to be in their twenties, die shortly after meeting the Enterprise crew. When the landing party returns to the Enterprise, the aging acceleration begins to affect each of them... except Chekov, who remains curiously immune.

Charles Drake (Commodore George Stocker)
Sarah Marshall (Dr. Janet Wallace)
James Doohan (Lt. Cmdr. Montgomery Scott)
George Takei (Lt. Hikaru Sulu)
Nichelle Nichols (Lt. Uhura)
Majel Barrett (Nurse Christine Chapel)
Walter Koenig (Ensign Pavel Chekov)
Felix Locher (Robert Johnson)
Carolyn Nelson (Yeoman Doris Atkins)
Laura Wood (Elaine Johnson)
Beverly Washburn (Lt. Arlene Galway)

• Stocker orders the ship to Starbase 10, crossing the Neutral Zone, where the Enterprise is attacked by Romulans. Stocker falls apart, but a healthy Kirk saves the day by using the "The Corbomite Maneuver".
  
• A competency hearing is called to relieve Kirk of duty. In the later series, the chief medical officer can relieve the captain if he is unfit without holding a hearing. (The sequence is rather lengthy and brings the already poorly-paced story to a halt.)
  
• Chekov was immune because he was scared when he found the dead body; the adrenaline kept him from aging. Lt. Galway died fairly quickly.
  
• Like many of the female guest stars, Dr. Janet Wallace once had a love affair with Kirk. When they broke up, she married Theodore Wallace, who was 26 years older than her and died recently. After Kirk started aging, Janet realized she still loved Kirk.
  
• Kirk states that he is 34 years old.