We discuss the discovery reach of CERN LEP 2 for the Higgs sector of a general extension of the MSSM including a single gauge singlet field. This change introduces a new quartic Higgs boson self-coupling which can increase the masses of the CP-even states, and also allows mixing between singlet and nonsinglet states which can reduce the couplings of the mass eigenstates to the Z. The lightest CP-even Higgs boson is bounded by a parameter {Λ} which takes a maximum value Λₘₐₓ{} 136--146 GeV for a top quark mass of 150--195 GeV. We generalize the discussion of the bound to include the entire CP-even spectrum and show how experiment may exclude values of {Λ} smaller than some Λₘᵢₙ. CP-even Higgs boson searches at LEP 2 will be able to exclude Λₘᵢₙ{} 81--105 GeV, depending on the machine parameters. We also present exclusion plots in the mA-tan{β} plane, based on an analysis of CP-even, CP-odd, and charged Higgs boson production processes at LEP 2. {} 1996 The American Physical Society.
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