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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 t_α and t_γ are observed for the LuAG:Pr SCF/LuAG:Sc SC composite scintillator with various film thicknesses. Furthermore, the best t_γ/t_α 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.