People with congenital prosopagnosia (CP) report difficulty recognising faces in everyday life and perform poorly on face recognition tests. Here, we investigate whether impaired adaptive face space coding might contribute to poor face recognition in CP. To pinpoint how adaptation may affect face processing, a group of CPs and matched controls completed two complementary face adaptation tasks: the figural aftereffect, which reflects adaptation to general distortions of shape, and the identity aftereffect, which directly taps the mechanisms involved in the discrimination of different face identities. CPs displayed a typical figural aftereffect, consistent with evidence that they are able to process some shape-based information from faces, e.g., cues to discriminate sex. CPs also demonstrated a significant identity aftereffect. However, unlike controls, CPs impression of the identity of the neutral average face was not significantly shifted by adaptation, suggesting that adaptive coding of identity is abnormal in CP. In sum, CPs show reduced aftereffects but only when the task directly taps the use of face norms used to code individual identity. This finding of a reduced face identity aftereffect in individuals with severe face recognition problems is consistent with suggestions that adaptive coding may have a functional role in face recognition.