Executive producer: Gene Roddenberry
Associate producers: Edward K. Milkis and Gregg Peters
Producer Fred Freiberger
Co-producer: Robert H. Justman
Story consultant: Arthur H. Singer

Writer: Jerome Bixby
Dir.: Murray Golden

Captain Kirk: William Shatner
Science Officer, First Officer, Cmdr. Spock: Leonard Nimoy
Dr. Leonard "Bones" Mc Coy: DeForest Kelly
Lt. Sulu: George Takei
Lieutenant Commander Montgomery Scott: James Doohan
Lieutenant Uhura: Nichelle Nichols
Rayna Kapec: Louise Sorel
Flint: James Daly

Stardate 5843.7

Holberg 917–G. In search for ryetalyn, the only antidote for the deadly Rigellian fever, which is plaguing the Enterprise, Kirk, Spock and McCoy beam down to the planet. The planet is supposed to unhinabited, but they are suddenly attacked by a strange robot, which cause thier weapon to be uneffective. They are about to be overwhelmed, when a man comes and stops the robot.  He introduces himself as Flint and orders them to leave, but when Dr. McCoy describes the symptoms of the feaver, he gives in and offers to have his robot to collect the ryetalyn for and invites them to his home. 

In the house, Kirk, Spock and McCoy are astonished to find pieces of art which date back more than 6,000 years. There also are original paintings of Leonardo which appears to be have been newly painted and yet they look authentic. Spock is so amazed that he accepts a drink. While they talk they are watched by Rayna, Flint's young protege. They are the first strangers she ever did see and she begs Flint to allow her to meet them. He would rather avoid any contact between the young woman and the other men, but, then, realizing how excited she is, he thinks better of it. By now, M4, the robot, has collected the ryetalyn and Flint offers his lab and equipment to transform it in the necessary drug. He also invites them to dinner; Kirk is about to decline, but then Rayna is introduced and he changes his mind.  

While McCoy leaves with M4 to see after the lab process, Flint encourages Kirk to get acquainted with Rayna and Spock to play a waltz so that they will dance. Later, McCoy comes back and says the ryetalyn collected by the robot is not good for their needs, because it's contaminad by an other element which will make it uneffective. Flint apologizes and says he will fetch an other load and analyze it himself. He leaves with McCoy and Spock tries to call his captain's attention on an other inexplicable fact - the waltz he just played is handwritten by Brahms (he states he knows the handwritting), it is totally unknown, but written with modern ink. Kirk seems more interested in Rayna and goes after her.   

Kirk finds Ryna in front of a closed door. He asks her what is in, but she doesn't know and can't really explain why she is driven to it. While Flint is watching them through a mirror, Kirk, seeing her confusion and willing to confort her, embrace and kisses Rayna, who responds. Suddenly he is attacked by the robot, which ignores Rayna's orders to stop and is destroyed by Spock. Flint explains that M4 has mistaken Kirk's attentions to Rayna for a threat. He also warns Kirk against trying to defy him, stating he has a great strength. Later Rayna questions him about the incident. She suspects he purposedly sent the robot after Kirk. Flint denies it and says the Enterprise men are about to leave and they will never come back. He allows her to go to say them goodby. Deaf to Spock's advices, Kirk tries to persuade her to go with him. 

Suddenly, the new ryetalyn, which was ready to be used, is nowhere to be found. Kirk, Spock and McCoy go looking for it and, following Spock's tricorder readings, find themselves in front of the forbidden door. They guess that Flint wants them to enter. Spock tries to convince his companions to allow him to go in alone, but to no avail. Inside, they discover many discharged half built androids, all looking like Rayna and understand the truth - Rayna is also an android, built by Flint who wanter for himself "the perfect woman". Flint joins them and finally explains - he was born on Earth about 6,000 years ago, he was woundend to death in war, but didn't die. He discovered to be immortal and lived many lives. He's Leonardo, Brahms and many others. He had had to change his personal appearance again and again and was now glad to have found a place where to stay for good. Being alone he made himself an android-woman and taught her all he knew. He needed an immortal woman to live with. He admits to have used Kirk to awake Rayna's feelings. What he is missing is that, just beacause of her newborn feelings, Rayna is a real woman and he no longer can control her will. 

Again, Kirk tries to convince her to go with him. Flint doesn't agrre and a fight start between him and Kirk. While they fight, Rayna dies because she cannot stand or understand the emotions inside her and she cannot handle the strange new situation. Now, since Rayna is dead, Flint leaves with the Enterprise to share his knowledge with other people. McCoy finds out that, having left the Earth and its fields, which caused the immortality, Flint will now age eventually die. Spock cannot see his captain suffer by remembering the woman he truly loved. Finding his friend asleep of exhaustion at his desk, he gently approaches and uses the Vulcan mind melt to help Kirk overcome the painful memory of Rayna.