In two experiments, typically developing (TD) children, high-functioning children with autism (HFA) and children with a history of autism who have achieved optimal outcomes (OOs), matched on age (M = 13 years) and nonverbal IQ, were asked to extend properties of categories to new items (categorical induction). All groups demonstrated some knowledge of category structure by extending at above-chance levels; however, the TD group extended more consistently than the OO and HFA groups. More consistent extenders had higher lexical and nonverbal IQ scores (Experiment 1) or higher pragmatics scores (Experiment 2). Thus, even very high functioning individuals with autism, or with an OO, still exhibit residual difficulties with category knowledge and extension; moreover, category tasks relate to a variety of verbal and nonverbal abilities. The difficulty these groups had with categorical induction may be related to their difficulty with generalization more widely; future research should investigate this possibility.