  In this work we present a model for the photoconductivity of two-dimensional
electron system in a perpendicular homogeneous magnetic field, a weak lateral
superlattice, and exposed to millimeter irradiation. The model includes the
microwave and Landau contributions in a non-perturbative exact way, the
periodic potential is treated perturbatively. The Landau-Floquet states provide
a convenient base with respect to which the lattice potential becomes
time-dependent, inducing transitions between the Landau-Floquet levels. Based
on this formalism, we provide a Kubo-like formula that takes into account the
oscillatory Floquet structure of the problem. The total conductivity exhibits
strong oscillations, determined by $\epsilon = \omega / \omega_c$ with $\omega$
the radiation frequency and $\omega_c$ the cyclotron frequency. The
oscillations follow a pattern with minima centered at $\omega/\omega_c =j +
{1/2} (l-1) + \delta $, and maxima centered at $\omega/\omega_c =j + {1/2}
(l-1) - \delta $, where $j=1,2,3.......$, $\delta$ is a constant phase shift
and $l$ is the dominant multipole contribution. Negative conductance states
develop as the electron mobility and the intensity of the microwave power are
increased. It is proposed that, depending on the geometry, negative conductance
sates or negative resistance states may be observed in lateral superlattices
fabricated in $GaAs/AlGa As$ heterostructures.
