One-phonon states with Kπ=0− and 1− are calculated within the RPA taking the isoscalar and isovector particle-hole and particle-particle octupole and isovector particlehole dipole interactions into account. General equations of the Quasiparticle-Phonon Nuclear Model are modified. The energies and wave functions of the nonrotational states below 2.3 MeV in 160Gd calculated within this model are in good overall agreement with experimental data. The E1 transition rates in several doubly even well-deformed nuclei are calculated. The influence of the radial dependence of the dipole and octupole interactions on E1 and E3 transition probabilities is investigated. It is shown that the fragmentation of one-phonon states below 2.3 MeV weakly affects the E1 transition rates from 1− states to the ground state. The fragmentation of one- and two-phonon states strongly affect B(E1) values of the transitions from 1− states with energy above 2.5 MeV to the ground states and between excited states. The results of calculating the E1 transition rates are compared with the relevant experimental data.