  The extended RPA theories are analyzed from the point of view of the problem
of stability of their solutions. Three kinds of such theories are considered:
the second RPA and two versions of the quasiparticle-phonon coupling model
within the time-blocking approximation: the model including 1p1h*phonon
configurations and the two-phonon model. It is shown that stability is ensured
by making use of the subtraction method proposed previously to solve double
counting problem in these theories. This enables one to generalize the famous
Thouless theorem proved in the case of the RPA. These results are illustrated
by an example of schematic model.
