  We consider L-violating Supersymmetric Models to explain the recent muon
$g_{\mu} -2$ deviation from the Standard Model. The order of trilinear
L-violating couplings which we require also generate neutrino mass which is
somewhat higher than expected unless one considers highly suppressed $L-R$
mixing of sfermions. However, without such fine tuning for sfermions it is
possible to get appropriate muon $g_{\mu}-2$ deviation as well as neutrino mass
if one considers some horizontal symmetry for the lepton doublet. Our studies
show that $g_{\mu} -2$ deviation may not imply upper bound of about 500 GeV on
masses of supersymmetric particles like chargino or neutralino as proposed by
other authors for R parity conserving supersymmetric models. However, in our
scenario sneutrino mass is expected to be light ($\sim 100$ GeV) and
$e-\mu-\tau$ universality violation may be observed experimentally in near
future.
