Under a strong ac drive the zero-frequency linear response dissipative resistivity [Formula presented] of a homogeneous state is allowed to become negative. We show that such a state is absolutely unstable. The only time-independent state of a system with a [Formula presented] is characterized by a current which almost everywhere has a magnitude [Formula presented] fixed by the condition that the nonlinear dissipative resistivity [Formula presented]. As a result, the dissipative component of the dc-electric field vanishes. The total current may be varied by rearranging the current pattern appropriately with the dissipative component of the dc-electric field remaining zero. This result, together with the calculation of Durst et al., indicating the existence of regimes of applied ac microwave field and dc magnetic field where [Formula presented], explains the zero-resistance state observed by Mani et al. and Zudov et al.