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.