  We consider here the spin independent neutralino-proton cross section for a
variety of SUGRA and D-brane models with R-parity invariance. The minimum cross
section generally is >~ 1\times 10^{-(9-10)} pb (and hence accessible to future
detectors) except for special regions of parameter space where it may drop to
=~ 10^{-12} pb. In the latter case the gluino and squarks will be heavy (>~ 1
TeV).
