  The influence of wave frequency variation on the anomalous cyclotron
resonance $\omega=\omega_{Be}+kv_{\|}$ interaction (ACRI) of energetic
electrons with a ducted finite amplitude whistler-mode wave propagating through
the so-called transient plasma layer (TPL) in the magnetosphere or in the
ionosphere is studied both analytically and numerically. The anomalous
cyclotron resonance interaction takes place in the case when the whistler-mode
wave amplitude $B_{W}$ is consistent with the gradient of magnetic field
$\overrightarrow{B_0}$. The region of phase space occupied by anomalously
interacting energetic electrons (synchronous particles) is determined. The
efficiencies of both the pitch-angle scattering of resonant electrons and their
transverse acceleration are studied and the efficiencies dependence on the
magnitude and sign of the wave frequency drift is considered. It has been shown
that in the case of ACRI occuring under conditions relevant to VLF-emission in
the magnetosphere, the energy and pitch-angle changes of synchronous electrons
may be enchanced by a factor $10^2 \div 10^3$ in comparison with ones for
nonsynchronous resonant electrons. So the small in density group of synchronous
particles may give significant contribution to a whistler-mode wave damping in
TPL.
