We study the production of the lightest neutralinos in the radiative process $e^+e^- to tildechi^0_1 tildechi^0_1gamma$ in low energy supersymmetric models for the International Linear Collider energies. This includes the minimal supersymmetric standard model as well as its extension with an additional chiral Higgs singlet superfield, the nonminimal supersymmetric standard model. We compare and contrast the dependence of the signal cross section on the parameters of the neutralino sector of the minimal and nonminimal supersymmetric standard model. We also consider the background to this process coming from the Standard Model process $e^+e^- to u bar u gamma$, as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) $e^+e^- to tilde u tilde u^ast gamma$, which can be a background to the radiative neutralino production when the sneutrinos decay invisibly. In low energy supersymmetric models radiative production of the lightest neutralinos may be the only channel to study supersymmetric partners of the Standard Model particles at the first stage of a linear collider, since heavier neutralinos, charginos and sleptons may be too heavy to be pair-produced at a $e^+ e^-$ machine with $sqrt{s} =500GeV$.
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