This study examined and compared the rhetorical structure of argumentative texts written by three groups of university students: 1) twenty Indonesian texts written by Indonesian native speakers (I.I.); 2) ten English texts written by Indonesian native speakers (I.E.); 3) ten English texts written by English native speakers (A.E.). Following the argumentative text analysis model developed by Tirkonnen-Condit (1984 and 1986) and Connor (1990), the data were analysed using top-down and bottom-up analysis techniques at macro organizational text level. The results indicated that the text organizational structure of argumentative texts in English and in Indonesian were different in respect of the frequency of occurence of sections-introductions, evaluation and conclusion and of the sub-sections of refutation, sub-claim, and induction within the problem section. Cultural differences between English and Indonesian may have played a crucial role in the text rhetorical differences. Also, the I.E. texts features are more similar to those of A.E. texts than to those of I.I. texts. The study indicates that the Indonesian students need to study the conventions of rhetorical structures and text features of English argumentative texts in order to be able to write good argumentative texts in English.