Claire falls in love as a young girl with an older Henry who has known her for many years, but when she meets him in her twenties, he is her age and has never met her before. She begins a relationship with a younger Henry who has yet to become the man she has fallen in love with, just as an older Henry spends his time caring for a young Claire who is alone in the cold atmosphere of her family's home, but is not the woman he leaves behind when he comes to "visit".
They cannot reveal Henry's illness for fear of his being locked up in a mental institution or taken away for study, so they tell few people. Other people weave in and out of the story: his violinist father, who has become an alcoholic recluse since his mother's death in a car accident when Henry was a young boy (a scene he revisits against his wishes). The housekeeper who helped to raise Henry when his father withdrew. Claire's bohemian friends who wonder and even disapprove of her husband who seems dark and even violent to them.
Claire and Henry go through an agonizing process trying to conceive, something Henry is hesitant about for fear of passing on his gift/curse. He goes so far as to have a vasectomy, but a past self comes along and helps Claire to conceive. A daughter is born, and the baby helps to reintegrate Henry's father into their lives. Henry meets with a doctor that he is able to convince of his disease and they go about studying it, they are never able to halt it, but they are able to identify the gene in Henry that they believe makes his time-travel possible.
A few years after the birth of his daughter, Henry's trips become more dangerous and violent, he senses a degeneration in his body from all the stress. One night he is suddenly thrust into freezing conditions, with no way to reach help. He contracts hypothermia before he travels back and he loses his feet. He and Claire both know what this means: without the ability to run; to steal clothing and money, to escape from danger, Henry will die.
One night Henry travels back to Claire's childhood and sees himself die, shot by her father and brother when they are out hunting. Later he travels to the future and meets his daughter on a school field trip and realizes he has died several years ago. He stays and gets to know his daughter for a while, she too can travel but she can control it to some degree, and she has found it more a gift than a curse. Claire hurries across town to try and see him, but he disappears before they can meet.
Now knowing when he dies, and that it is soon, he gathers all his friends and family for a big party, saying goodbye without telling them, then he sits in Claire's arms and spends his last minutes with her. He disappears and then comes back seemingly moments later, fatally wounded.
Claire is despondent but she lives for the few times that Henry has traveled to the future and thus will still be in her life. He visits a couple of times, but he sees their daughter more than her. He promises her that he will come for her on the day she dies. Claire spends the rest of her life, and she has spent it thus far, waiting for Henry.