The results of the study of the contributions of the interaction reactions of fast neutron sources of 239Pu-Be and 252Cf to the counting efficiency of registration by oxide scintillators CdWO4, ZnWO4, Bi4Ge3O12 and Gd2SiO5, presented. The amount of gamma quanta per input neutron emitted from final nuclei excited in the reactions of inelastic scattering (n, nʹγ)in, resonant scattering (n, n)res and capture (n, γ)res and radiation capture (n, γ)cap was measured. PMT R1307 operating in single-electron mode was used as a photodetector, the background rate was ~ 5*103 s-1. The measured efficiency ε for scintillators ø40x40 mm was 752 for ZWO, 532 for CWO, 37 for GSO, and 23 for BGO in "counts/neutron" units, measurement error rate ~ 3-5%. The formation of the detector response is influenced by the parameters of the scintillator nuclei, such as the values of the interaction cross sections in the resonance region, the density of nuclear levels of the final nuclei, the lifetime of excited nuclear states, the upper limit of the resonance region of the cross section, as well as the scintillation time and geometric parameters of the scintillators. A phenomenological model of the response of an oxide scintillator to fast neutrons is proposed.