Introduction Prosody has been little studied in the primary progressive aphasias (PPAs), a group of neurodegenerative disorders presenting with progressive language impairment. Methods Here we conducted a systematic investigation of different dimensions of prosody processing (acoustic, linguistic and emotional) in a cohort of 19 patients with nonfluent PPA syndromes (11 with progressive nonfluent aphasia, PNFA; five with progressive logopenic/phonological aphasia, LPA; three with progranulin-associated aphasia, GRN-PPA) compared with a group of healthy older controls. Voxel-based morphometry (VBM) was used to identify neuroanatomical associations of prosodic functions. Results Broadly comparable receptive prosodic deficits were exhibited by the PNFA, LPA and GRN-PPA subgroups, for acoustic, linguistic and affective dimensions of prosodic analysis. Discrimination of prosodic contours was significantly more impaired than discrimination of simple acoustic cues, and discrimination of intonation was significantly more impaired than discrimination of stress at phrasal level. Recognition of vocal emotions was more impaired than recognition of facial expressions for the PPA cohort, and recognition of certain emotions (in particular, disgust and fear) was relatively more impaired than others (sadness, surprise). VBM revealed atrophy associated with acoustic and linguistic prosody impairments in a distributed cortical network including areas likely to be involved in perceptual analysis of vocalisations (posterior temporal and inferior parietal cortices) and working memory (fronto-parietal circuitry). Grey matter associations of emotional prosody processing were identified for negative emotions (disgust, fear, sadness) in a broadly overlapping network of frontal, temporal, limbic and parietal areas. Conclusions Taken together, the findings show that receptive prosody is impaired in nonfluent PPA syndromes, and suggest a generic early perceptual deficit of prosodic signal analysis with additional relatively specific deficits (recognition of particular vocal emotions).