We consider the hypothesis of the existence of a class of short (10−2-10−3s) and weak (10−6-10−7erg/s· cm2) γ-bursts of cosmological origin. These events arise from gravitational microlensing of bright, quiet γ-ray sources (with luminosity about 3·1038erg/s) located in distant (z ≥ 1) galaxies by stars inside foreground galaxies. If the size of the γ-ray sources is 104-106cm, motion with respect to the observer or the intermediate galaxy may bring them close to the neigborhood of cusps along critical curves generated by individual stars (corresponding to caustics in the observer’s plane). In these cases the observed fluxes increase by a factor 1011-1013, the temporal variation of intensity being due to the brightness distribution in the source and to the distance from the cusp (in the source plane). Using standard assumptions for the number and sizes of “quiet” γ-ray sources, the number and characteristics of galaxies, we estimate the observed burst rate to be between 1 and 10 bursts per year (see below). Their temporal and spectral properties are determined by the nature of sources (ejecting pulsar, accreting neutron star with a weak or strong magnetic field, black hole) and by their velocity relative to the cusp. Similar effects have been discussed in the context of flux variability and structure studies of quasars (e.g. Schneider & Weiss 1986, Grieger et al. 1988, Refsdal & Surdej 1994). However, in these cases the source sizes were larger than 1014cm3 and amplification did not exceed 102.