  Within the framework of the Next-To-Minimal Supersymmetric Standard Model
(NMSSM) we study neutralino production $e^+e^- \longrightarrow \tilde{\chi}^0_i
\tilde{\chi}^0_j$ ($i,j=1,\ldots ,5$) at center-of-mass energies between 100
and 600 GeV and the decays of the heavier neutralinos into the LSP plus a
fermion pair, a photon or a Higgs boson. For representative gaugino/higgsino
mixing scenarios, where the light neutralinos have significant singlet
components, we find some striking differences between the NMSSM and the minimal
supersymmetric model. Since in the NMSSM neutralino and Higgs sector are
strongly correlated, the decay of the second lightest neutralino into a Higgs
boson and the LSP often is kinematically possible and even dominant in a large
parameter region of typical NMSSM scenarios. Also, the decay rates into final
states with a photon may be enhanced.
