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We study the production of the lightest neutralinos in the radiative process$e^+e^- \to \tilde\chi^0_1 \tilde\chi^0_1\gamma$ in low energy supersymmetricmodels for the International Linear Collider energies with longitudinallypolarized electron and positron beams. For this purpose we consider the case ofnonminimal supersymmetric standard model as well as the case of minimalsupersymmetric standard model. At the first stage of a linear collider, with$\sqrt{s} =500$ GeV, the radiative production of the lightest neutralinos maybe a viable channel to study supersymmetric partners of the Standard Modelparticles, especially if the other supersymmetric particles are too heavy to tobe pair-produced. We consider in detail the effect of beam polarization on theproduction cross section. We compare and contrast the dependence of the signalcross section on the parameters of the neutralino sector of the nonminimal andminimal supersymmetric standard model when the electron and positron beams arelongitudinally polarized. In order to assess the feasibility of experimentallyobserving the radiative neutralino production process, we consider thebackground to this process coming from the Standard Model process $e^+e^- \to\nu \bar\nu \gamma$ with longitudinally polarized electron and positron beams.We also consider the supersymmetric background to the radiative neutralinoproduction process coming from the radiative production of the scalar partnersof the neutrinos (sneutrinos) $e^+e^- \to \tilde\nu \tilde\nu^\ast \gamma$,with longitudinally polarized beams. This process can be a a background to theradiative neutralino production when the sneutrinos decay invisibly.

Radiative neutralino production in low energy supersymmetric Models. II. The case of beam polarization