Alpha and gamma spectroscopy (pulse height spectra and scintillation decay time profiles) were used to study scintillating properties of composite scintillators systems consisting of single crystalline films (SCF) and single crystal (SC) substrate plates. α-particles of 241Am of energy 5.4857 MeV and γ-quanta of 137Cs of energy 661.66 keV are used as excitation sources of SCFs or SC substrates, respectively. As SC substrates mainly LuAG:Pr single crystal plates are used and these plates are characterized by light yield (LY) between 10-21 × 103 ph/MeV, Energy Resolution (ER) ~5% at 661.66 keV and good proportionality. LuAG:Ce, Lu2-xGdTbxAG:Ce and Lu3-xTbxAG:Ce SCFs at x = 0.15–2.285 were prepared by LPE method onto LuAG:Pr substrates and investigated. LY of LuAG:Ce SCF under α-particles excitation is about of 60% than that of LuAG:Pr SC substrate. The LY of Lu3-x TbxAG:Ce SCFs depend nonlinearly on Tb3+ concentration in the 0.15–2.285 range and changed from 60-62% to 106–109%, respectively, in comparison with LY of LuAG:Pr SC substrate. Detailed scintillation decay time profiles have shown that there are differences between the decay curves of composite scintillators under α-particles and γ-quanta excitations. Such differences are characterized using the tα/tγ ratio between the time of scintillation decay to 1/e, 0.1, 0,05 and 0.02 levels under α-particles excitation (tα) and γ-quanta excitation (tγ). From all studied types of composite scintillators, based on the LuAG:Pr substrates, the highest value of tα/tγ ratio can be reached for Lu3-xTbxAG:Ce SCF/LuAG:Pr SC substrate composite scintillators at Tb content x = 2.15–2.275, where this ratio is equal to 4.2–6.2 at scintillation decay level of 0.1. •Pulsed height spectra under α- and γ-rays were used to study scintillating properties.•α-particles of 241Am allow to excite only single crystalline films as LuAG:Ce and LuAG:Ce,Tb.•Ratio of tα/tγ scintillation decay intensities should be the highest for new prepared Lu3-xTbxAG:Ce garnets.•Composite scintillators can to resolve various of parts ionizing radiation components as α-particles, ions or γ-quanta.