E. Caliceti(*), F. Cannata(**), S. Graffi(*) Perturbation theory of PT-symmetric Hamiltonians (34K, LaTeX 2e) ABSTRACT. In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by $\PT$symmetric additional interactions.