  We analyze the Higgs intense--coupling regime, in which all Higgs particles
of the Minimal Supersymmetric Standard Model are light with masses of the same
order and the value of $\tb$ the ratio of vacuum expectation values of the two
Higgs fields is large, in the framework of Supergravity scenarios with
non--universal soft Supersymmetry breaking scalar masses in the Higgs sector.
In particular, we calculate the relic density abundance of the lightest
neutralino candidate for cold dark matter and the rates in direct and indirect
detection at present and future experiments. We first show that while in the
mSUGRA model this regime is disfavored by present data, there are regions in
the parameter space of models with non--universal Higgs masses where it can
occur. We then show that because of the large value of $\tan\beta$ and the
relatively low values of the neutral Higgs boson masses, the cross section for
neutralino--nucleon scattering is strongly enhanced in this regime and would
allow for the observation of a signal in direct detection experiments such as
CDMS--Soudan. The expected sensitivity of gamma--ray detectors like GLAST might
be also sufficient to observe the annihilation of neutralinos in such a regime.
