  We examine the recently observed deviation of the muon g - 2 from the
Standard Model prediction within the framework of gravity mediated SUGRA models
with R parity invariance. Universal soft breaking (mSUGRA) models, and models
with non-universal Higgs and third generation squark/slepton masses at M_G are
considered. All relic density constraints from stau-neutralino co-annihilation
and large \tan\beta NLO corrections for b \to s\gamma decay are included, and
we consider two possibilities for the light Higgs: m_h > 114 GeV and m_h > 120
GeV. The combined m_h, b \to s\gamma and a_{\mu} bounds give rise to lower
bounds on \tan\beta and m_{1/2}, while the lower bound on a_{\mu} gives rise to
an upper bounds on m_{1/2}. These bounds are sensitive to A_0, e.g. for m_h >
114 GeV, the 95% C.L. is \tan\beta > 7(5) for A_0 = 0(-4m_{1/2}), and for m_h >
120 GeV, \tan\beta > 15(10). The positive sign of the a_{\mu} deviation implies
\mu > 0, eliminating the extreme cancellations in the dark matter
neutralino-proton detection cross section so that almost all the SUSY parameter
space should be accessible to future planned detectors. Most of the allowed
parts of parameter space occur in the co-annihilation region where m_0 is
strongly correlated with m_{1/2}. The lower bound on a_{\mu} then greatly
reduces the allowed parameter space. Thus using 90% C. L. bounds on a_{\mu} we
find for A_0 = 0 that \tan\beta \geq 10 and for \tan\beta \leq 40 that m_{1/2}
= (290 - 550) GeV and m_0 = (70 - 300) GeV. Then the tri-lepton signal and
other SUSY signals would be beyond the Tevatron Run II (except for the light
Higgs), only the \tilde{\tau}_1 and h and (and for part of the parameter space)
the \tilde{e}_1 will be accessible to a 500 GeV NLC, while the LHC would be
able to see the full SUSY mass spectrum.
