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 , Phys. Rev. Lett. 98, 106804 (2007)].