  Searches for the Standard Model Higgs boson by the four LEP experiments found
excess events in two mass ranges: a 2.3 sigma excess around 98 GeV, and an 1.7
sigma excess around 115 GeV. The latter has been discussed widely in the
literature, but the former has attracted little attention so far. In this paper
I explore the possibility of explaining the excess near 98 GeV through
production of the lighter CP--even Higgs boson in the Minimal Supersymmetric
Standard Model (MSSM). It is shown that this allows to simultaneously explain
the excess near 115 GeV through the production of the heavier CP--even MSSM
Higgs boson. The resulting light Higgs sector offers opportunities for charged
Higgs boson searches at the Tevatron and LHC. Neutral Higgs boson searches at
the LHC in the di--muon channel are also promising. However, conclusive tests
of this scenario may have to wait for the construction of a linear e+ e-
collider.
