  The theorem on the existence of maximal nonnegative invariant subspaces for a
special class of dissipative operators in Hilbert space with indefinite inner
product is proved in the paper. It is shown in addition that the spectra of the
restrictions of these operators on the corresponding invariant subspaces lie in
the closed upper half-plane. The obtained theorem is a generalization of
well-known results of L.S.Pontrjagin, H.K.Langer, M.G.Krein and T.Ja.Azizov
devoted to this subject.
