  A classical model for {\em dc} transport of two dimensional electrons in a
perpendicular magnetic field and under strong irradiation is considered. We
demonstrate that, near the cyclotron resonance condition, and for {\em linear}
polarization of the {\em ac} field, a strong change of the diagonal component,
$\sigma_d$, of the {\em dc} conductivity occurs in the presence of a {\em weak}
nonparabolicity of the electron spectrum. Small change in the electron
effective mass due to irradiation can lead to negative $\sigma_d$, while the
Hall component of the {\em dc} conductivity remains practically unchanged.
Within the model considered, the sign of $\sigma_d$ depends on the relative
orientation of the {\em dc} and {\em ac} fields, the sign of the detuning of
the {\em ac} frequency from the cyclotron resonance, and the sign of
nonparabolic term in the energy spectrum.
