Impairments in both theory of mind (ToM; the ability to attribute mental states to oneself and others) and executive function (EF; a group of high-level cognitive functions which help guide and control goal-directed behaviour) have been demonstrated in individuals with autism spectrum disorders (ASDs). Both deficits have been proposed by different groups of researchers as being the single primary cognitive deficit of autism, which can subsume the other deficit as secondary or artefactual. However, few studies have examined the nature of the relationship between ToM and EF in ASDs or conducted a systematic investigation of their relative primacy. This research principally sought to establish the primacy and independence of impairments in ToM and EF in ASDs and thereby evaluate the validity of single versus multiple primary deficit models of autism. These aims were addressed in two studies, both broad in scope. The first study was an investigation of the profile, primacy, and independence of ToM and EF impairments in individuals with ASDs. The sample included 46 participants with ASDs and 48 control participants matched on age and non-verbal ability. The profile of impairments was examined by measuring ToM and a range of EF components using tasks employing, wherever possible, process-pure indices of performance. Primacy was measured by focussing on i) whether or not the deficits observed were universal among individuals with ASDs; ii) whether the deficits were able to discriminate individuals with ASDs from matched controls (i.e., predict group membership); and iii) the ability of ToM and EF deficits to explain the full range of autistic symptomatology, as measured by correlating cognitive performances with behavioural indices. The relationship between ToM and EF impairments was investigated by conducting correlations between ToM and EF variables as well as analysing the incidence of dissociations between impairments in the two domains. The ASD group was found to demonstrate significant impairments in ToM and several components of EF including planning, verbal inhibition, working memory (in a context where inhibitory control was required), and both verbal and non-verbal generativity. However, neither ToM nor EF impairments were able to meet all of the criteria for a primary deficit in ASDs. EF deficits were found to be more primary, but could not account for ToM as a secondary deficit, as ToM and EF were found to be independent (i.e., uncorrelated and dissociable) deficits in the ASD group. This pattern of results suggested that a multiple deficits model involving at least two independent impairments appeared to best characterise ASDs, but the data were compatible with several variants of such a model (e.g., involving distinct subtypes versus a multidimensional spectrum). The second study was an investigation of ToM and EF impairments in siblings of individuals with ASDs, who have previously been found to demonstrate a subclinical “broad autism phenotype”. The main aims of this study were i) to identify whether ToM or EF deficits could meet criteria for an “endophenotype” or vulnerability marker for the autism genotype in unaffected relatives, which would have further implications about the primacy of ToM and EF in ASDs; and ii) to further investigate the validity of various multiple deficits models of ASDs by examining the pattern of ToM and EF performance in those showing the broad phenotype. Participants were 108 siblings of individuals with ASDs and 67 siblings of controls, tested on the same ToM and EF tasks used in the first study. Confirming the superior primacy of EF deficits found in Study One, there was no significant difference in ToM performance between ASD and control siblings, but ASD siblings showed weaknesses on two measures of EF. Furthermore, there appeared to be different subgroups of siblings demonstrating different cognitive profiles, consistent with the heterogeneity evident in the first study. This research indicated that ASDs cannot be explained by a single primary cognitive deficit. These findings hold important theoretical and empirical implications and highlight further questions about which type of multiple deficits model might best explain ASDs.