This study investigated the nature of the second language acquisition (SLA) of eight international PhD students that occurred as they undertook the literature review when planning their doctoral research projects at a New Zealand university. While the social, cultural approaches have been seen as broadening the field of SLA by introducing diverse epistemologies (Ortega, 2012), their conceptions of the mind and cognition of the second language speaker as a social product, and of SLA as the outcome of social processes (see Atkinson, 2011a), appear to be problematic in terms of understanding the central mechanisms of SLA. This study addresses this issue by explicating the mind and cognition of the participants and their SLA from a phenomenological realist perspective. Central to the theoretical framework for the study are Husserl’s (1970) realist ontology and epistemology, Widdowson’s (1983, 1990) theory of language learning through the negotiation of meaning and Bruce’s (2008a) identification of extra-linguistic and linguistic areas of genre knowledge in an English-medium academic context while developing their literature reviews (LR). Interpretative phenomenological analysis (Smith, Flowers & Larkin, 2009) was used as the overarching methodology to investigate the ontology of the participants, their epistemological processing, and their acquisition of academic English. This involved analysing monthly interviews with individual participants and supplementary data collected during a six-month conditional enrolment period. In addition, an analysis of the actual LR texts of five participants was undertaken to examine the textual outcomes of the LR process. This analysis focused, in particular, on genre knowledge and logicality as critical elements of the academic competence that the participants were engaged in developing. The findings of the study suggest that intentionality as a cognitive process was what enabled the participants to engage with social processes in the course of their SLA. Thought and language, as two separate entities in the knowledge of the participants, seemed to interact hierarchically in the process of undertaking the LR. Their SLA seemed to occur through this hierarchical thought-language operation, which involved participants drawing on and using new linguistic and procedural resources to express their thought. In addition, the thought of the participants seemed not to be constrained or regulated by linguistic and rhetorical systems (either from their first language or English). Rather, in their efforts to engage with disciplinary knowledge when processing and communicating the meaning of academic texts intended by the authors, participants went beyond such cultural frames. Significantly, this meaning-uncovering intentionality appeared to facilitate parallel SLA. While advice and feedback from other members of their particular community appeared to be important to their SLA, it was not evident that social interaction was the central, facilitative process. Moreover, the overall findings of the study suggest a need to expand the scope of what constitutes SLA in academic contexts. That is, developing competence in using academic English appeared to involve not only the acquisition of linguistic resources, but also developing extra-linguistic genre knowledge that ensures textual coherence, in order to communicate intended thought including logicality and criticality successfully.