  A method to implement realistic nucleon-nucleon residual interaction (Bonn CD
force) based on the Brueckner G-matrix into the Quasiparticle Random Phase
Approximation (QRPA) for deformed nuclei is formulated. The two-neutrino double
decay for ground state to ground state transitions $^{76}$Ge$ \to ^{76}$Se and
$^{150}$Nd $\to ^{150}$Sm is calculated along with the Gamow-Teller strength
distributions. The effect of deformation on the observables is studied.
