The energy spectrum of the elementary excitations arising in the three-component excitonphoton-phonon system in the presence of a macroscopic large coherent exciton mode is considered, supposing the Bose-Einstein condensation of excitons on the single particle state with wave vector k = 0. The Green's functions describing the system in the frame of the Belyaev diagram technique obey to a set of Dyson equations. There are three initial branches of the noninteracting subsystems. They have the form of the Bogolyubov type excitonic spectrum, phonon branch and photon spectrum counted from the chemical potential value. In the six points of their intersections a strong reconstruction of the spectrum takes place. In three of them the spectrum is stable. Here simple and evanescent waves can exist. In the other three points of intersections absolute or non-convective instabilities of the spectrum appear.