  We show that the use of forward proton detectors at the LHC installed at 220
m and 420 m distance around ATLAS and / or CMS can provide important
information on the Higgs sector of the MSSM. We analyse central exclusive
production of the neutral CP-even Higgs bosons h and H and their decays into
bottom quarks, tau leptons and W bosons in different MSSM benchmark scenarios.
Using plausible estimates for the achievable experimental efficiencies and the
relevant background processes, we find that the prospective sensitivity of the
diffractive Higgs production will allow to probe interesting regions of the
M_A--tan_beta parameter plane of the MSSM. Central exclusive production of the
CP-even Higgs bosons of the MSSM may provide a unique opportunity to access the
bottom Yukawa couplings of the Higgs bosons up to masses of M_H \lsim 250 GeV.
We also discuss the prospects for identifying the CP-odd Higgs boson, A, in
diffractive processes at the LHC.
