  The $2\nu\beta\beta$-decay running sums for $^{76}$Ge and $^{150}$Nd nuclei
are calculated within a QRPA approach with account for deformation. A realistic
nucleon-nucleon residual interaction based on the Brueckner G matrix (for the
Bonn CD force) is used. The influence of different model parameters on the
functional behavior of the running sums is studied. It is found that the
parameter $g_{pp}$ renormalizing the G matrix in the QRPA particle-particle
channel is responsible for a qualitative change in behavior of the running sums
at higher excitation energies. For realistic values of $g_{pp}$ a significant
negative contribution to the total $2\nu\beta\beta$-decay matrix element is
found to come from the energy region of the giant Gamow-Teller resonance. This
behavior agrees with the results of other authors.
