[en] On the basis of a stochastic model of filling up the electron-hole capture centres following irradiation, the kinetics of light sum accumulation in crystallophosphors with any number of capture levels has been considered. Using as an example a crystallophosphor with two hole- and two electron capture centres, solution of equations for the kinetics of light sum accumulation in solid dosemeters is presented. It is shown that in the presence of two competing capture centres the filling-up of one of the traps is always described by the function with a bent and superlinear section, whereas the filling-up of the competing trap is described by the function without a bent. The dose-effect functional relationship for competing traps does not depend either on the energetic depth of the trap or absolute values of capture micro cross-sections, but depends solely on relative values of macro- and micro cross-sections for competing traps. The theoretical model has been checked when studying radiothermoluminescence of synthetic quartz. The experimental results are shown to agree well with the model suggested