Professionalisation, defined as the transmission of competences adapted to the job-market, is one of the new missions of Doctoral Schools in France. Interviews with supervisors reveal a number of ambivalent attitudes towards this new policy. Supervisors do support the rhetoric of professionalisation, but are powerless to push their students towards other careers than the academic one. We interpret this as a challenge to the academic identity through the modification of what a Ph.D is, which, in turn, impacts on the content, output and meaning of supervision. We show that academics do professionalise their students, but only for the profession they know: academia. They only train the students whom they believe they can acknowledge as future peers, and the on-the-job training provided by Ph.D supervisors is implicitly directed towards academia. The absence of an explicit academic professional identity is discussed, as well as the fact that "professionalising" must relate to a specific professional identity. We argue that only "specific" professional identity can be transmitted, leading to questions about the implementation of the related policy.