  We present a model for microwave photoconductivity in two-dimensional
electron systems (2DESs) in a magnetic field at the microwave frequencies lower
that the electron cyclotron frequency when the intra-Landau level (LL)
transitions dominate. Using this model, we explain the effect of decrease in
the 2DES dissipative conductivity (and resistivity) and smearing of its
Shubnikov -- de Haas oscillations by microwave radiation observed recently
\cite{1,2}. The model invokes the concept of suppression of elastic impurity
scattering of electrons by the microwave electric field. We calculated the
dependence of the 2DES conductivity associated with intra-LL transitions as a
function of the radiation and cyclotron frequencies and microwave power. The
obtained dependences are consistent with the results of recent experimental
observations \cite{1,2}.
