The aim of the present study is to compare the pragmatic ability of right- and left-hemisphere-damaged patients excluding the possible interference of linguistic deficits. To this aim, we study extralinguistic communication, that is communication performed only through gestures. The Cognitive Pragmatics Theory provides the theoretical framework: it predicts a gradient of difficulty in the comprehension of different pragmatic phenomena, that should be valid independently of the use of language or gestures as communicative means. An experiment involving 10 healthy individuals, 10 right- and 9 left-hemisphere-damaged patients, shows that pragmatic performance is better preserved in left-hemisphere-damaged (LHD) patients than in right-hemisphere-damaged (RHD) patients.