The kinetics of scintillation process in Czochralski-grown CaMoO4 crystals excited by α particles and γ rays from 238Pu and 137Cs radioactive isotopes, respectively, is investigated. Kinetics of scintillations is shown to be complex and multicomponent in character. Fast and slow scintillation components are observed, and their relative contributions to the total light yield in the scintillator are determined. The possibility is demonstrated of discriminating between scintillator signals due to α particles and γ rays.