  The recent discovery of the microwave induced vanishing resistance states in
a two dimensional electron system (2DES) is an unexpected and surprising
phenomena. In these experiments the magnetoresistance of a high mobility 2DES
under the influence of microwave radiation of frequency $\omega$ at moderate
values of the magnetic field, exhibits strong oscillations with zero-resistance
states (ZRS) governed by the ratio $\omega /\omega_c$, where $\omega_c$ is the
cyclotron frequency. In this work we present a model for the photoconductivity
of a two dimensional electron system (2DES) subjected to a magnetic field. The
model includes the microwave and Landau contributions in a non-perturbative
exact way, impurity scattering effects are treated perturbatively. In our
model, the Landau-Floquet states act coherently with respect to the oscillating
field of the impurities, that in turn induces transitions between these levels.
Based on this formalism, we provide a Kubo-like formula that takes into account
the oscillatory Floquet structure of the problem. We study the effects of both
short-range and long-range disorder on the photoconductivity. Our calculation
yields a magnetoresistance oscillatory behavior with the correct period and
phase. It is found that, in agreement with experiment, negative dissipation can
only be induced in very high mobility samples. We analyze the dependence of the
results on the microwave power and polarization. For high-intensity radiation
multi-photon processes take place predicting new negative-resistance states
centered at $ \omega / \omega_c=1/2$, and $ \omega / \omega_c= 3/2$.
