  The leading direct dark matter search experiments: CDMS, Edelweis and
DAMA/NaI exhibit different results for different approaches to the problem.
This contradiction can reflect a nontrivial and probably a multi-component
nature of the cosmological dark matter. WIMPs can possess dominantly a Spin
Dependent interaction with nucleons. They can be superheavy or represent
atom-like systems of superheavy charged particles. The Dark matter can contain
a component, which strongly interacts with the matter. We show that even a
moderate size superfluid $^3$He detector provides a crucial test for these
hypotheses and that its existing laboratory prototype is already of interest
for the experimental dark matter search.
