  We report on the observation of terahertz radiation induced edge
photogalvanic currents in graphene, which are nonlinear in intensity. The
increase of the radiation intensities up to MW/cm$^2$ results in a complex
nonlinear intensity dependence of the photocurrent. The nonlinearity is
controlled by the back gate voltage, temperature and radiation frequency. A
microscopic theory of the nonlinear edge photocurrent is developed. Comparison
of the experimental data and theory demonstrates that the nonlinearity of the
photocurrent is caused by the interplay of two mechanisms, i.e. by direct
inter-band optical transitions and Drude-like absorption. Both photocurrents
saturate at high intensities, but have different intensity dependencies and
saturation intensities. The total photocurrent shows a complex sign-alternating
intensity dependence. The functional behaviour of the saturation intensities
and amplitudes of both kinds of photogalvanic currents depending on gate
voltages, temperature, radiation frequency and polarization is in a good
agreement with the developed theory.
