  An analysis is given of the effects of non-universal soft SUSY breaking
masses in the Higgs sector and in the third generation squark sector, and it is
shown that they are highly coupled. Analytic expressions are obtained for their
effects on the parameters $\mu,m_A$ and on the third generation squark masses.
Non-universality effects on dark matter event rates in neutralino-nucleus
scattering are analysed. It is found that the effects are maximal in the range
$m_{\tilde\chi_1}\leq 65$~GeV where the relic density is governed by the Z and
Higgs poles. In this range the minimum event rates can be increased or
decreased by factors of O(10) depending on the sign of non-universality. Above
this range Landau pole effects arising from the heavy top mass tend to suppress
the non-universality effects. The effect of more precise measurements of
cosmological parameters on event rates, which is expected to occur in the next
round of COBE like sattelite experiments, is also investigated. Implications
for the analysis for dark matter searches are discussed.
