  The Weakly Interacting Massive Particle (WIMP) is the main candidate for the
relic dark matter. A set of exclusion curves currently obtained for cross
sections of the spin-dependent WIMP-proton and WIMP-neutron interaction is
given. A two-orders-of-magnitude improvement of the sensitivity of the dark
matter experiment is needed to reach the SUSY predictions for relic
neutralinos. It is noted that near-future experiments with the high-spin
isotope Ge-73 can yield a new important constraint on the neutralino-neutron
effective coupling and the SUSY parameter space.
