Reanalyses of LEP data have shown preference to two light CP-even Higgs
bosons. We discuss implications of such a Higgs boson spectrum for the minimal
supersymmetric model extended by a Standard Model singlet chiral superfield and
an additional Abelian gauge invariance (the U(1)' model). We, in particular,
determine parameter regions that lead to two light CP-even Higgs bosons while
satisfying existing bounds on the mass and mixings of the extra vector boson.
In these parameter regions, the pseudoscalar Higgs is found to be nearly
degenerate in mass with either the lightest or next-to-lightest Higgs boson.
Certain parameters of the U(1)' model such as the effective mu parameter are
found to be significantly bounded by the LEP two-light-Higgs signal.Comment: 20 pp, 7 figs, 2 table