We consider the SUSY-model neutralino as a dominant Dark Matter partic
le in the galactic halo and investigate some general issues of direct
DM searches via elastic neutralino-nucleus scattering. On the basis of
conventional assumptions about the nuclear and nucleon structure, wit
hout referring to a specific SUSY-model, we prove that it is impossibl
e in principle to extract more than three constraints on fundamental S
USY-model parameters from the direct Dark matter searches. Three types
of Dark matter detectors probing different groups of parameters are r
ecognized.