Study of the shift of two-phonon poles in deformed nuclei by the method of boson expansions

New phonons are constructed by the boson expansion method. The model Hamiltonian is expressed through the new phonon operators up to the fourth order terms. The two-phonon pole shift is calculated. It coincides up to the main terms with that calculated with the RPA phonons and strict inclusion of the Pauli principle. This result confirms the absence of collective two-phonon states in even-even deformed nuclei.