The bimolecular ionization of photoexcited molecules is theoretically investigated assuming the light pumping of moderate intensity is either instantaneous or permanent. The kinetics of energy quenching and ion-radical accumulation and recombination after delta -pulse excitation are studied beyond the rate concept, in the framework of Integral Encounter Theory (IET). The results are compared with those obtained within extended Unified Theory (UT), contact and Markovian approximations, and a widely accepted exponential model. When there is a shortage of accepters the theory becomes nonlinear and discloses the striking effect of electron-transfer saturation. In such conditions and under permanent illumination IET is the sole formalism appropriate for a full time-scale (non-Markovian) description of system relaxation. The original program for solving nonlinear IET equations for particle concentrations was developed and first used to calculate the kinetics of relaxation to equilibrium and to a stationary regime. The non-Markovian corrections to the quantum yields of fluorescence and charge separation obtained numerically are in good correspondence with analytic estimates of these quantities.