  Neutralinos with a large singlino component may appear in extended
supersymmetric models with additional singlet Higgs fields. Since singlinos do
not couple to (s)fermions and gauge bosons, the cross sections for the
production of singlino dominated neutralinos are generally small. Within the
framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) and an
E_6 inspired model we study neutralino production e^+ e^- --> neutralino_1
neutralino_2 (neutralino_1,2 neutralino_3) with a singlino dominated
neutralino_2 (neutralino_3). It is shown that neutralinos with a singlino
contribution up to 99 % can be produced with a cross section larger than 1 fb
and may therefore be detected at a high luminosity e^+ e^- linear collider even
if they are not the LSP.
