The literature surrounding the autistic child's social impairment is reviewed. It is proposed that an impairment in some aspect of autistic children's social cognition could account for many of the observed abnormalities in their social behaviour. First, two "lower-level" aspects of social cognition are considered. These are mirror self-recognition and perceptual role-taking. The present sample of autistic children did not differ from MA control groups in either of these respects, confirming results from other studies. A "higher-level" aspect of self-other differentiation is conceptual role-taking. This ability is also called a "theory of mind". This literature is reviewed and a hypothesis is proposed which suggests that autistic children have an impairment in their "second-order" representational capacity which has been argued to underlie a theory of mind. This hypothesis is explored by means of 4 experiments. These showed that autistic children's "first-order" representational capacity, as manifested in their understanding of physical causality, is intact whilst their second-order representational capacity, as manifested in their ability to attribute mental states to others, is impaired. This deficit was not found in controls. Furthermore, those few autistic children who passed a test of attribution of belief at the ii year old level, failed at the ("third-order") 7 year old level, despite adequate MA. Pretend play can be related to conceptual role-taking, since both may require a second-order representational capacity. The literature surrounding the autistic child's impairment in pretend play is reviewed and the final experiment confirms and extends previous results in this domain. It is concluded that particular aspects of the social impairment and the impairment in pretend play can be seen as the result of a deficit in one cognitive mechanism. This deficit is discussed in terms of what has loosely been called an "impaired symbolic capacity".