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Using time-resolved luminescence spectroscopy, excitation density effects were investigated under conditions of resonant creation of excitons by femtosecond laser pulses in CdWO4 scintillator at room temperature. It was revealed that the decay kinetics of intrinsic emission becomes accelerated and deviates from the exponential law in the initial stage due to the Förster dipole-dipole interaction of self-trapped excitons. It is shown that these processes originate from the relaxed exciton states even at excitation power up to ~1012 W/cm2. The quantitative analysis of the experimental data is performed, and the dipole-dipole interaction parameters discussed. The results obtained are shown to be of general importance for understanding the problem of nonproportional response of scintillators, whose operation is based on intrinsic luminescence.