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The scintillation properties of novel type of composite scintillator based on Lu3Al5O12:Pr (LuAG:Pr) single crystalline film (SCF) and LuAG:Sc substrate grown by the liquid-phase epitaxy method are considered in this work. The registration of α-particles and γ-quanta in such types of composites occurs by means of separation of the scintillation decay kinetics of SCF and crystal parts, respectively. Namely, under excitation by α-particles of 241Am (5.5 MeV) source and γ-quanta of 137Cs (662 keV) source, the large differences in the respective scintillation decay kinetics and decay time values tα and tγ are observed for the LuAG:Pr SCF/LuAG:Sc SC composite scintillator with various film thicknesses. Furthermore, the best tγ/tα ratio above 4.5 is achieved for such types of epitaxial structure with SCF and substrate thicknesses of 17 μm and about 0.5 mm, respectively. The development types of composite scintillators can be successfully applied for simultaneous registration of α-particles and γ-quanta in the mixed radiation fluxes.