In this paper we have studied a mechanism for radiation damage of gas phase molecules of glycine [Gly] and dipeptide derivatives of glycine, such as diglycine [Gly-Gly], cyclo(glycylglycyl) [cyclo(Gly-Gly)] and glycyl-leucine [Gly-Leu] by the impact of He2+ ions with energy Ep = 4 keV/u. Relative cross sections of different elementary processes occurring in single collisions between dipeptide derivatives of glycine and ions have been measured for the first time. The fragmentation channels of both singly and multiply charged molecular ions have been studied experimentally. It has been shown that in the process of Gly-Gly sublimation, cyclization in the crystalline sample takes place, which results in formation of cyclo(Gly-Gly). Using the DFT method, the geometry of molecules and singly charged ions of glycine dipeptide derivatives has been calculated, as well as energies of different experimentally observed fragmentation channels of these ions.