« If you want to sell what the client buys, you should see the world through the client’s eyes!... » To what extend this evident Marketing and Value Management rule is true for the Non-for-Profit Organisations of Enterprise Development Support subjected to the inter-cultural contact, whether it would be an accompanying agency for the immigrant entrepreneurs in France or an international enterprise development mission in a transitional economy country? To bring some elements of reply to this question, the authors are basing on the ethno-methodological observations, as well as on the action-research, realised in frame and for the account of such organisations. As a result, they suggest that these organisations and their staff members are to realise a simultaneous double appropriation effort. Indeed, the appropriation endeavour is necessary in regards with both, the classical management tools usage but also the intercultural variable. It is shown that, in the case of the Accompanying to the immigrant enterprise creators in France, their interaction with the Accompanying structure appears to be complicated by a supplementary intercultural psychological arbitration. This process, in turn, influences the accompanying agent. Subsequently, the relation between the Entrepreneur and the Support Provider could be described as a co-appropriation relation: the support provider has to appropriate the entrepreneur’s project, his cultural identity and his Acculturation strategy, while the entrepreneur is to appropriate the corresponding management tools of enterprise creation. Such co-appropriation constitutes a necessary condition for the true efficacy of the above Provider-Entrepreneur relation. Thus, this intercultural support relationship is modelled in terms of a dynamic matrix that is presently used as a management tool at one of the French entrepreneurial support devices (Boutiques de Gestion). The authors then discuss its possible transposition on the international aid programs for Enterprise (SME) Development Support in the transitional countries and the consequences of such transposition