  We investigate the potential of current and planned hadron colliders
operating at the TeV scale in disentangling the structure of the Higgs sector
of non-minimal Supersymmetric extensions of the Standard Model with an extra
gauge singlet. We assume universality of the soft Supersymmetry breaking terms
at the GUT scale as well as a CP-even Higgs boson with mass around 115 GeV, as
suggested by LEP. We find that mixing angles between the doublet and singlet
Higgs states are always small. However, concrete prospects exist at both the
Tevatron (Run II) and the Large Hadron Collider of detecting at least one
neutral Higgs state with a dominant singlet component, in addition to those
available from a doublet Higgs sector which is similar to the one of the
Minimal Supersymmetric Standard Model.
