We report on observation of pronounced terahertz radiation-induced magnetoresistivity oscillations in AlGaAs/GaAs two-dimensional electron systems, the terahertz analog of the microwave induced resistivity oscillations (MIRO). Applying high-power radiation of a pulsed molecular laser we demonstrate that MIRO, so far observed at low power only, are not destroyed even at very high intensities. Experiments with radiation intensity ranging over five orders of magnitude from 0.1 to 104W/cm2 reveal high-power saturation of the MIRO amplitude, which is well described by an empirical fit function I/(1+I/Is)β with β∼1. The saturation intensity Is is of the order of tens of watts per square centimeter and increases by a factor of 6 by increasing the radiation frequency from 0.6 to 1.1 THz. The results are discussed in terms of microscopic mechanisms of MIRO and compared to nonlinear effects observed earlier at significantly lower excitation frequencies.