  Magnetoresistance oscillations in two-dimensional electron systems driven
simultaneously by a strong direct current and a microwave irradiation, are
analyzed within a unified microscopic scheme treating both excitations on an
equal footing. The microwave-induced resistance oscillations are described by a
parameter $\epsilon_\omega$ proportional to the radiation frequency, while the
dc-induced resistance oscillations are governed by a parameter $\epsilon_j$
proportional to the current density. In the presence of both a microwave
radiation and a strong dc, the combined parameter $\epsilon_\omega+\epsilon_j$
is shown to control the main resistance oscillations, in agreement with the
recent measurement [Zhang {\it et al.} Phys. Rev. Lett. {\bf 98}, 106804
(2007)]
