Abstract. We show that a real Hopf *-algebra with a positive and faithful Haar measure has a faithful *-representation on a real Hilbert space. Such quantum groups are generalizations of compact quantum groups, because the notion of realC*-algebra generalizes that of complexC*-algebra (the quantum groupSLq(n,R) is an example of this type). We deduce from this result an improvement of Hochschild's version of the functionnal Tannaka-Krein theorem. We also give a reductivity criterion for a Hopf algebra over a field of characteristic zero, which we use to obtain a characterization of finite type group algebras.