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. (Contains 5 tables and 1 note.)