The delusional belief that a close relative has been replaced by a look-alike impostor was named the Capgras delusion in honor of Joseph Capgras, who described the first case. Capgras's original patient, Mme M., had a complex mental illness with various symptoms in addition to the delusion of substitution. The focus in the literature has always been on her eponymous delusion, ignoring the rest of her condition. However, studying the substitution delusion in isolation from the rest of her illness has led to inadequate conclusions. It is necessary to understand the delusion within the broad context of her illness. Toward that goal, her mental illness is described here in detail. A particular pattern of delusions and illness is identified. This same pattern is noted in other cases of Capgras in the literature. Three new cases are reported here, each with the same overall pattern of illness that Mme M. had. This pattern is labeled the Syndrome of Capgras. A hypothesis is offered to explain the Capgras delusion within the context of this illness.