  We present a model for microwave photoconductivity of two-dimensional
electron systems in a magnetic field which describes the effects of strong
microwave and steady-state electric fields. Using this model, we derive an
analytical formula for the photoconductivity associated with photon- and
multi-photon-assisted impurity scattering as a function of the frequency and
power of microwave radiation. According to the developed model, the microwave
conductivity is an oscillatory function of the frequency of microwave radiation
and the cyclotron frequency which turns zero at the cyclotron resonance and its
harmonics. It exhibits maxima and minima (with absolute negative conductivity)
at the microwave frequencies somewhat different from the resonant frequencies.
The calculated power dependence of the amplitude of the microwave
photoconductivity oscillations exhibits pronounced sublinear behavior similar
to a logarithmic function. The height of the microwave photoconductivity maxima
and the depth of its minima are nonmonotonic functions of the electric field.
It is pointed to the possibility of a strong widening of the maxima and minima
due to a strong sensitivity of their parameters on the electric field and the
presence of strong long-range electric-field fluctuations. The obtained
dependences are consistent with the results of the experimental observations.
