Non-Minimal Supersymmetric Higgs Bosons at LEP2

We discuss the discovery reach of LEP2 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 non-singlet states which can reduce the couplings of the mass eigenstates to the $Z$. The lightest CP-even Higgs boson is bounded by a parameter $\Lambda$ which takes a maximum value $\Lambda_{max}\approx 136-146$ GeV for top mass $150-195$ GeV. We generalise the discussion of the bound to include the entire CP-even spectrum and show how experiment may exclude values of $\Lambda$ smaller than some $\Lambda_{min}$. CP-even Higgs boson searches at LEP2 will be able to exclude $\Lambda_{min}\approx 81-105$ GeV, depending on the machine parameters. We also present exclusion plots in the $m_A-\tan\beta$ plane, based on an analysis of CP-even, CP-odd and charged Higgs production processes at LEP2.