  We study radiative neutralino production e^+e^- \to \tilde\chi^0_1
\tilde\chi^0_1\gamma at the linear collider with longitudinally polarised
beams. We consider the Standard Model background from radiative neutrino
production e^+e^- \to \nu \bar\nu \gamma, and the supersymmetric radiative
production of sneutrinos e^+e^- \to \tilde\nu \tilde\nu^\ast \gamma, which can
be a background for invisible sneutrino decays. We give the complete tree-level
formulas for the amplitudes and matrix elements squared. In the Minimal
Supersymmetric Standard Model, we study the dependence of the cross sections on
the beam polarisations, on the parameters of the neutralino sector, and on the
selectron masses. We show that for bino-like neutralinos longitudinal polarised
beams enhance the signal and simultaneously reduce the background, such that
statistics is significantly enhanced. We point out that there are parameter
regions where radiative neutralino production is the only channel to study SUSY
particles, since heavier neutralinos, charginos and sleptons are too heavy to
be pair-produced in the first stage of the linear collider with \sqrt{s}=500
GeV.
