In this work we study the microwave photoconductivity of a two-dimensional electron system (2DES) in the presence of a magnetic field and a two-dimensional modulation (2D). 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 longitudinal conductivity and resistivity exhibit strong oscillations, determined by ϵ = ω/ω(c), with ω the radiation frequency and ω(c) the cyclotron frequency. The oscillations follow a pattern with minima centred at [Formula: see text], and maxima centred at [Formula: see text], where j = 1,2,3..., δ∼1/5 is a constant shift and l is the dominant multipole contribution. Negative resistance states (NRSs) develop as the electron mobility and the intensity of the microwave power are increased. These NRSs appear in a narrow window region of values of the lattice parameter (a), around a∼l(B), where l(B) is the magnetic length. It is proposed that these phenomena may be observed in artificially fabricated arrays of periodic scatterers at the interface of ultraclean GaAs /Al(x)Ga(1-x)As heterostructures.