From Damn Interesting:
A person with Capgras’ Syndrome suffers from the delusion that one or more of their close friends or family members have been replaced with exact duplicates, and they cannot be shaken from this belief in spite of an otherwise clean bill of mental health. In some instances, the person believes that they themselves are, in whole or in part, a duplicate. Unlike the paranoia expected from such a condition, there is never a motive assigned for the appearance of the duplicates – the patients do not believe someone is “out to get them,” but they are at a loss for an explanation why anyone would want to replace their loved ones.
This odd misperception is named after the French psychiatrist Jean Marie Joseph Capgras, who described the case of a Madame M. in 1923. The woman insisted that identical-looking persons had taken the place of her family. Over time her delusion expanded to include neighbors, friends and acquaintances. But Madame M. never bothered to get to know these impostors because it was her belief that each one regularly left to make room for the next double. In all, she eventually claimed to have had more than eighty husbands.