  To show the existence of precursor phenomena of the transition order$\
to$chaos in atomic nuclei a simple analysis has been made, based on a recent
criterion proposed by Pavli\-chenkov. The basic idea is that nonlinear effects
in rotational bands should lead to bifurcation, which qualitatively changes the
spectrum for one of the nuclear excitation branches. Experimental data
concerning the isotopes of Er, Hf, Yb, Os, Dy, W strongly support the above
criterion.
