Academic supervision of PhD dissertations and master's theses has traditionally been conceptualised as the pedagogy of the dyadic relationship between master and apprentice. Recently, researchers have argued for a more systemic approach. Yet, many communities lack practices for sharing the pedagogical responsibility of supervision. Consequently, individual teachers face the challenges of supervision alone. We have been involved in university pedagogical training where these challenges are explored. Data consist of 44 academics' learning tasks, from which we analysed to what extent and how supervision is interpreted as a social activity, and what kind of cultural elements appear in the teachers' discourses. We adopted the sociocultural approach to discourse analysis and treat the academics' experiences as reflections of their wider culture. A "traditional supervisory discourse" pervaded much of the challenges we identified in the academics' descriptions; however, there was also evidence of an aspiring "process-orientated dialogical supervision discourse."