  A collective Hamiltonian for the rotation-vibration motion of nuclei is
considered, in which the axial quadrupole and octupole degrees of freedom are
coupled through the centrifugal interaction. The potential of the system
depends on the two deformation variables $\beta_2$ and $\beta_3$. The system is
considered to oscillate between positive and negative $\beta_3$-values, by
rounding an infinite potential core in the $(\beta_2,\beta_3)$-plane with
$\beta_2>0$. By assuming a coherent contribution of the quadrupole and octupole
oscillation modes in the collective motion, the energy spectrum is derived in
an explicit analytic form, providing specific parity shift effects. On this
basis several possible ways in the evolution of quadrupole-octupole
collectivity are outlined. A particular application of the model to the energy
levels and electric transition probabilities in alternating parity spectra of
the nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.
