  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.
