The Josephson photoresponse of a current biased granular Tl2Ba2CaCu2O8 thin film has been measured at 4.2 K for radiation frequencies ω in the range 20–111 cm-1. The resulting photosignal s depends nonlinearly on the incident power P satisfying the relationship s=K(ω)Pα(ω), where K is a frequency-dependent constant. The value of α increases monotonically from 0.5 at 20.2 cm-1 to 0.9 at 111 cm-1. At 20.2 cm-1 this power law is valid for incident powers between 5 mW and 1 kW, a range of more than 105. These limits are imposed by experimental constraints and not by deviations from the power-law behavior. As the frequency increases, the responsivity of the film drops strongly, K(ω) decreasing approximately as ω-3, so that the power-law validity is established over three orders of magnitude at 111 cm-1. Such a behavior of the Josephson photoresponse has been previously observed, albeit over reduced dynamic ranges, in granular superconducting films of other materials. Thus we believe it to be an inherent characteristic of the random arrays of Josephson junctions contained in such films.