  The dynamics of nuclear collective motion is investigated in the case of
reflection-asymmetric shapes. The model is based on a new parameterization of
the octupole and quadrupole degrees of freedom, valid for nuclei close to the
axial symmetry. Amplitudes of oscillation in other degrees of freedom different
from the axial ones are assumed to be small, but not frozen to zero. The case
of nuclei which already possess a permanent quadrupole deformation is discussed
in some more detail and a simple solution is obtained at the critical point of
the phase transition between harmonic octupole oscillation and a permanent
asymmetric shape. The results are compared with experimental data of the
Thorium isotopic chain. The isotope Th-226 is found to be close to the critical
point.
