Neidhardt H., Zagrebnov V.A. On the right Hamiltonian for singular perturbations: general theory. (70K, LateX) ABSTRACT. We show that,using the notion of the maximal(with respect to perturbation) Friedrichs extension of unperturbed operator, one can classify the problem of construction of the ``right Hamiltonian''as well-posed or ill-posed in dependence on the intersection of the quadratic form domain of perturbation and deficiency subspace corresponding to restriction of unperturbed operator to stability domain.