  We study the central diffractive production of the (three neutral) Higgs
bosons, with a rapidity gap on either side, in an MSSM scenario with
CP-violation. We consider the bb-bar and tautau-bar decay for the light H_1
boson and the four b-jet final state for the heavy H_2 and H_3 bosons, and
discuss the corresponding backgrounds. A direct indication of the existence of
CP-violation can come from the observation of either an azimuthal asymmetry in
the angular distribution of the tagged forward protons (for the exclusive pp ->
p+H+p process) or of a sin(2phi) contribution in the azimuthal correlation
between the transverse energy flows in the proton fragmentation regions for the
process with the diffractive dissociation of both incoming protons (pp ->
X+H+Y). We emphasise the advantage of reactions with the rapidity gaps (that is
production by the pomeron-pomeron fusion) to probe CP parity and to determine
the quantum numbers of the produced central object.
