How is the content of university programs selected and structured? How does it evolve? In the anthropological theory of the didactic, external didactic transposition designates the processes through which knowledge to be taught is delimited and developed for delivery within a school institution, including universities. This paper presents a first international comparative research project focused on the external didactic transposition in European and Canadian undergraduate programs in mathematics. The project aims at analyzing the factors that motivate the evolutions of the programs, the procedures to develop them, as well as the constraints that limit broader modifications and can explain their current state. The exploratory study presented in this paper considers 10 case studies from universities in Canada, Denmark, France, Germany, and Spain. Data is mainly collected from semi-structured interviews with faculty having participated in recent design of undergraduate mathematics programs and syllabi. We identify both similarities and differences between programs and syllabi, with the differences being relatively significant between Canadian and European universities when it comes to the overall structure of programs, and less visible when considering the European programs, as well as the processes in general.