In 1893 London, England, popular writer Herbert George "H.G." Wells (Malcolm McDowell) displays a time machine to his skeptical dinner guests. After explaining how it works (including a "non-return key" that keeps the machine at the traveler's destination and a "vaporizing equalizer" that keeps the traveler and machine on equal terms), police constables arrive at the house searching for the serial killer Jack the Ripper. One finds a bag, with blood-stained gloves, belonging to one of Herbert's friends, a surgeon named John Leslie Stevenson (David Warner), whom they are unable to locate in the house, concluding that Stevenson might be the infamous killer. Wells races to his laboratory, but the time machine is gone.Stevenson has escaped to the future, but because he does not have the "non-return" key, it automatically returns to 1893. Herbert uses it to pursue Stevenson to November 5, 1979, where the machine has ended up on display at a museum in San Francisco realizing that due to the machine traveling backwards by the geographic longitide and latitude, the machine had ended up in the unfamiliar USA. As Herbert walks around the city, he is deeply shocked by the future, having expected it to be an enlightened socialist utopia, only to find chaos in the form of airplanes, automobiles and a worldwide history of war, crime and bloodshed.Searching numerous banks for Stevenson - he believes an Englishman might need to exchange old currency - Herbert meets liberated Chartered Bank of London employee Amy Robbins (Mary Steenburgen). She directs Herbert to the Hyatt Regency hotel, as she previously had Stevenson.Confronted in his room by his onetime friend Herbert, Stevenson confesses that he finds modern society to be pleasingly violent. Apologetically, he states: "Ninety years ago, I was a freak. Now... I'm an amateur." Herbert demands he return with him to 1893 to face justice, but Stevenson, who without the "return key" would be unable to prevent the machine from automatically returning (and thereby blocking Herbert from any further pursuit), attempts to wrest it from him. Their struggle is interrupted by a hotel employees and Stevenson flees, getting hit by a car during the frantic chase on foot. Herbert follows him to the San Francisco General Hospital emergency room and mistakenly gets the impression that Stevenson had died from his injuries.Herbert meets up with Amy Robbins again and she is the aggressor in a romance (succeeding, once Herbert is sure that she is in earnest). Stevenson returns to the bank to exchange more money. Rightly concluding that it was Amy who had led Herbert to him, he finds out where she lives. Herbert, hoping to convince her of the truth, takes a highly skeptical Amy three days into the future. Once there, she is aghast to see a newspaper headline revealing her own murder as the Ripper's fifth victim (a temporal paradox).Herbert persuades her that they must go back - it is their duty to attempt to prevent the fourth victim's murder, then prevent Amy's. However, they are delayed upon their return to the present and can do no more than phone the police. Stevenson kills again, and Herbert is arrested because of his knowledge of the killing. Amy is left alone, totally defenseless, and at the mercy of the "San Francisco Ripper."At the police station, Herbert unsuccessfully tries to convince the police of Amy's peril (his claim to be "Sherlock Holmes" has marked him as a lunatic well before mentioning a "time machine"). At the same time, Amy attempts to hide from Stevenson. When the police finally do investigate her apartment, they find the dismembered body of a woman. Since he was in custody at the time Herbert is released having been cleared as a suspect. As Herbert wonders the dark streets mourning Amy's brutal death, he is suddenly confronted by Stevenson, who has actually killed Amy's co-worker Carol, who had accepted an invitation for dinner and to meet Wells. Stevenson then kidnapped Amy in order to extort the time machine key from Wells.Stevenson flees with the key - and Amy as insurance - to attempt a permanent escape in the time machine. Herbert gives chase in a car (despite not driving very well while Stevenson forces Amy to drive her car at gunpoint). Breaking into the museum, Herbert bargains for Amy's life, she is able to escape. As Stevenson starts up the time machine with the key, Herbert removes the "vaporizing equalizer" from the machine and Stevenson nods in understanding. The removal of this component, Herbert had confirmed earlier, causes the machine to remain in place while its passenger is sent traveling endlessly through time, with no way to stop; in effect sending him to oblivion.Herbert proclaims that the time has come to return to his own time, by himself, in order to destroy a machine that is too dangerous for primitive mankind. Amy pleads with him to take her along (despite her aversion to living in Victorian England). As they depart back to the past, she says that she is changing her name to Susan B. Anthony. The end credits reveal that the two later married.