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We describe a large-signal performance of novel high-power radio frequency (RF) switches based on III-nitride insulated gate metal-oxide semiconductor heterostructure field-effect transistors (MOSHFETs). The maximum switching powers for a single MOSHFET with only 1-mm gate width exceed 50W at 10GHz, more than an order of magnitude higher than those achievable using GaAs transistors. In the ON state, the highest powers are determined by the device peak drain currents, 1-2A/mm for the state-of-the art III-N MOSHFETs; in the OFF state their maximum powers are limited by the breakdown voltage, normally well above 100V. Our experimental data are in close agreement with large-signal simulations and the proposed simple analytical model. We also show that the insulating gate design allows for broader bandwidth and higher switching powers and better stability as compared to conventional Schottky gate transistors.