We study the production of the lightest neutralinos in the radiative process [Formula: see text] in supersymmetric models with grand unification. We consider models wherein the standard model (SM) gauge group SU(3)c×SU(2)L×U(1)Yis unified into the grand unified gauge groups SU(5) or SO(10). We study this process at energies that may be accessible at a future International Linear Collider (ILC). We compare and contrast the dependence of the signal cross-section on the grand unified gauge group, and different representations of the grand unified gauge group, into which the SM gauge group is unified. We carry out a comprehensive study of the radiative production process which includes higher-order QED corrections in our calculations. In addition we carry out a detailed study of the background to the signal process coming from the SM radiative neutrino production [Formula: see text], as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) [Formula: see text]. The latter can be a major supersymmetric background to the radiative production of neutralinos when the sneutrinos decay invisibly. It is likely that the radiative production of the lightest neutralinos may be a viable channel to study supersymmetric partners of the SM particles at the first stage of an ILC, where heavier sparticles may be too heavy to be produced in pairs.