The prospects for central exclusive diffractive (CED) production of MSSM Higgs bosons at the LHC are reviewed. It is shown that the CED channels, making 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. In particular, CED production of the neutral CP-even Higgs bosons h and H and their decays into bottom quarks has the potential to probe interesting regions of the M_A--tan_beta parameter plane of the MSSM and may give access to the bottom Yukawa couplings of the Higgs bosons up to masses of M_H approx 250 GeV.
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