Theory of light absorption and circular photocurrent in Weyl semimetals is developed for arbitrary large light intensities with account for both elastic and inelastic relaxation processes of Weyl fermions. The direct optical transition rate is shown to saturate at large intensity, and the saturation behaviour depends on the light polarization and on the ratio of the elastic and inelastic relaxation times. The linear-circular dichroism in absorption is shown to exceed 10~% at intermediate light wave amplitudes and fast energy relaxation. At large intensity $I$, the light absorption coefficient drops as $1/sqrt{I}$, and the circular photogalvanic current increases as $sqrt{I}$.
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