Drawing on Critical Discourse Analysis and, more specifically, on the relationship between the macro-level of dominant discourses and the micro-level of individual positionings, we examine the way linguistic identities are constructed by immigrant students of Albanian origin in Greece. We elaborate on two "competitive" discourses: the national, homogenizing one and the post-national, deconstructing one, and the way they influence the construction of immigrant students' linguistic identities. Our data come from lyceum immigrant students' essays which are analyzed in order to trace their positionings towards the two "competitive" discourses, and in particular, towards the linguistic dimension of these discourses. For a systematic investigation of immigrant students' linguistic identities we employ the membership categorization device "living populations in Greece" which includes the categories "immigrant people" and "majority people" as a standardized relational pair. We focus on the category-bound predicates of the category "immigrant people" and particularly on those related to the knowledge of the majority language. Our main finding is that the immigrant students of Albanian origin in our data are positively positioned towards the national, homogenizing discourse and particularly towards Greek monolingualism, thus looking forward to the social benefits of speaking Greek.