  The upper mass bound of the lightest neutral Higgs scalar is studied in the
$\mu$ problem solvable extra U(1) models by using the analysis of the
renormalization group equations. In order to restrict the parameter space we
take account of a condition of the radiative symmetry breaking and some
phenomenological constraints. We compare the bound obtained based on this
restricted parameter space with the one of the next to the minimal
supersymmetric standard model (NMSSM). Features of the scalar potential and
renormalization group equations of the Yukawa couplings among Higgs chiral
supermultiplets are rather different between them. They can reflect in this
bound.
