This paper reports on a study of the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper excerpts from the lectures of the seven participating teachers are analysed, using commognitive theory. Characteristic features of the teachers’ discourses about functions are presented, focusing on routines – repetitive patterns characteristic of the discourse. The discursive practices are found to contain two intertwined discourses – mathematical discourse and discourse of mathematics teaching. Routines specific to the mathematical discourse are construction and substantiation routines, while the didactical routines include motivation, explanation, activation and recall routines.