  We investigate phenomenology related to the neutral fields in supersymmetric
models with an extra U(1) derived from $E_6$. Our study is concentrated into
the models which have a singlino dominated neutralino as the lightest
superparticle (LSP). If such models satisfy a constraint for dark matter
derived from the WMAP data, the lightest neutral Higgs scalar, a new neutral
gauge field $Z^\prime$ and the LSP may be interesting targets for the study at
the LHC. We also discuss features of the $Z^\prime$ in the models and its
detectability at the LHC.
