Nonlinear interaction of electronic excitations has been shown to play a remarkable role in luminescent material performance. Recently, it has been intensely studied in semiconductors and wide-gap scintillators. The nonlinear interaction is a cause of the nonproportionality of scintillator response to the energy of the absorbed ionizing radiation and can limit its energy resolution, which results in crucial deterioration of the scintillator functionality. The type and degree of nonproportionality are material specific and depend little on impurity content or sample treatment. Theoretical models have been developed, which explain the effect of scintillator response nonproportionality by the interplay between the density and mobility of charge carriers created in a track of ionizing radiation [1-3]. Energy losses in relaxation processes and the final distribution of excited luminescence centres in a material are determined by a number of processes including thermalisation of hot carriers, their recombination, interaction, trapping at defects and impurities and exciton formation. In the present contribution, we demonstrate how the mutual interaction of small-radius Frenkel excitons created at high densities by ionizing radiation or intense laser pulses can reveal itself in the luminescence characteristics of a luminescent material. It is shown that the related phenomena observed in various materials under X or γ rays are similar to those detected under UV-XUV excitation, which allows their theoretical description proceeding from the same principles and their experimental study in substantially better controlled experimental conditions of excitation by ultrashort laser pulses with well-defined timing and spatial parameters. A remarkable effect of saturation of excitonic absorption was discovered under excitation by ultrashort UV pulses from the energy region of phonon-assisted electronic transitions. The changes in the luminescence decay kinetics and various saturation effects in excitonic and impurity luminescence induced by high-density or high-energy excitation are demonstrated and theoretically modelled for several wide-gap materials. The experimental results of this contribution originate mainly from the study of time-resolved luminescence in tungstate crystals of different structures, wolframites CdWO4 and ZnWO4, and homologous scheelites CaWO4, SrWO4, BaWO4, by using femtosecond UV-XUV sources such as free-electron lasers, tuneable femtosecond lasers, high-order harmonic generation systems. It is shown that the emission decay and saturation can be described within the frame of Förster’s dipole-dipole interaction model on the basis of theoretical statements developed in [1]. The importance of studying exciton-exciton interactions is demonstrated by revealing a direct link between the Förster interaction radius and nonproportionality of the material light response. A good correlation between the radius of cation, radius of exciton and radius of Förster interaction is shown for the sequence of homologous scheelites CaWO4, SrWO4, BaWO4.