In this chapter, we report on the various teaching strategies we use to facilitate the emergence of Intercultural Competences in two French Graduate Schools of Engineering, Telecom Bretagne and ENSIETA. Our two tier experiential teaching design creates a space for negotiation, with learning conditions which enable students to gain first hand experience of the realities of Intercultural Management and Communication (Morace and Gourvès-Hayward 2009). Using a concept called "interity", developed by Demorgon (2002, 2004, 2005), based on insights from the French philosopher and mathematician, Couturat (1905), we encourage the students to negotiate a common frame of reference and action. Our main objective is to use the diversity represented by cultural and personal differences within the student and teacher groups, to both co-construct knowledge and promote cultural awareness. We first describe our teaching design and its implementation in our particular context, taking into account student and lecturer profiles, objectives, contents, teaching methods and course organisation. Secondly, drawing on one of the central notions of sociocultural theory, that of learning as a mediated process, where the use of cultural tools and artefacts, both physical and symbolic, can transform and shape higher mental functioning in fundamental ways (Vygotsky 1981; Luria 1979; Wertsch 1985; Lantolf 2000; Kinginger 2001), we show how our students appropriate or reject the various forms of mediation made available to them. Thirdly, we analyse the Intercultural Competences which emerge throughout the experiential learning process, using the five savoirs developed by Byram and Zarate 1994 and Demorgon’s multiperspectivist approach. We conclude by assessing the pertinence of the various teaching strategies used and by recommending further improvements.