In previous tests of the lowest level of a "theory of mind" (i.e. first-order belief attribution), 80% of autistic children were found to be impaired relative to a non-autistic mentally-handicapped control group. The present study examines the 20% of autistic children who have a theory of mind at the lowest level, and tests their ability to use a theory of mind at higher levels (i.e. second-order belief attribution). This autistic subgroup, in comparison to Down's Syndrome and normal control groups, was found to be severely impaired at the higher level. Autism is discussed as a possible case of specific developmental delay.