  We present a nonperturbative quasi-classical theory of graphene
photoconductivity. We consider the influence of low-frequency (microwave,
terahertz, mid-infrared) radiation on the static conductivity of a uniform
graphene layer and calculate its photoconductivity as a function of frequency,
polarization and strength of the external ac electric field, as well as on the
material properties (electron density, scattering time) and temperature. The
theory is valid at frequencies $\hbar\omega\lesssim 2E_F$ and at arbitrarily
strong ac electric fields. We compare our results with those of the third-order
perturbation theory and determine the applicability range of the perturbative
solutions.
