We study the eect of inhomogeneities in Hall conductivity on the nature of the Zero Resistance States seen in the microwave irradiated two-dimensional electron systems in weak perpendicular magnetic elds, and we show that time-dependent domain patterns may emerge in some situations.For an annular Corbino geometry, with an equilibrium charge density that varies linearly with radius, we nd a time-periodic non-equilibrium solution, which might be detected by a charge sensor, such as an SET. For a model on a torus, in addition to static domain patterns seen at high and low values of the equilibrium charge inhomogeneity, we nd that, in the intermediate regime, a variety of nonstationary states can also exist. We catalog the possibilities we have seen in our simulations. Within a particular phenomenological model, we show that linearizing the nonlinear charge continuity equation about a particularly simple domain wall conguration and analyzing the eigenmodes allows us to estimate the periods of the solutions to the full nonlinear equation.