Two studies are reported in which the ability of people with Asperger's syndrome to understand problems of the type "Peter thinks that Jane thinks that ..." tested. The results showed that in contrast to younger or more handicapped autistic individuals, Asperger subjects were able to solve problems of the type just outlined, i.e. that they possessed a second-order theory of mind. When asked to explain their solutions however, they typically did not use mental state terms but did not differ in this respect either from non-handicapped or socially impaired, chronic schizophrenic controls. The implications of the results for current cognitive theories of autistic impairment are discussed.