A consistent theoretical approach is used to evaluate the contribution from the quasi-elastic knock-out and “spectator” mechanisms to the invariant spectra of α-particles produced under large angles by interactions of protons, deuterons and α-particles with energies of a few GeV/nucleon with 1p-shell nuclei. Effects of rescattering on nucleons, constituting the knocked-out fragment, the residual nucleus and the incident particle, are investigated. It is shown that in the framework of the quasi-elastic knock-out mechanism one can get a good description of the experimental spectra of α-fragments produced under angles of about 90° with energies from 20 up to 60 MeV. As the energy of the observed particle is increasing, the contribution from the mechanism considered is diminished, but it is still appreciable (up to 10%) for energies up to 180 MeV.