The present linguistic analyses of two children (aged 8 and 10) with Asperger Syndrome (AS) and their two matched controls are based on dyadic therapist-child conversations and on picture description tasks. The circa 100 analysis features covering aspects of (i) lexicon (e.g. prominalization), (ii) structural characteristics of turns, (iii) co-operation features (e.g. shared/non-shared elaboration of themes), (iv) prosody, (v) cognitive aspects (e.g. involvement/commitment, world of discourse) and (vi) affect features, show that the AS speakers describe, rather than narrate their conceptualizations, whether (practically) self-initiated (dyadic discourse) or prompted through pictures (narratives). In previous experimental studies of spatially deictic expressions and spatial orientation, it has been shown that the spatial and low-level social cognition of these AS subjects was unimpaired. However, in the present study AS discourse carries features of impaired inter-personal and inter-subjective performance, manifest, for example, in linguistic deixis, atypical power-oriented features and lack of joint activity.