  We systematically analyze the anomalous dipole $\Delta k_{\gamma}$ and
quadrupole $\Delta Q_{\gamma}$ moments of the W gauge bosons in the context of
the minimal supersymmetric standard model as functions of the soft SUSY
breaking parameters $A_0,m_0,M_{1/2}$ and the top quark mass. The severe
constraints imposed by the radiative breaking mechanism of the electroweak
symmetry\,$ SU(2)\times U(1)$\, are duly taken into account. The supesymmetric
values of $\Delta k_{\gamma}$ and $\Delta Q_{\gamma}$ can be largely different,
in some cases, from the standard model predictions but of the same order of
magnitude for values of \quad $A_0,m_0,M_{1/2} \leq {\cal O}(1 TeV) $.
Therefore possible supersymmetric structure can be probed provided the accuracy
of measurements for $\Delta k_{\gamma}$, $\Delta Q_{\gamma}$ reaches
$10^{-2}-10^{-3}$ and hence hard to be detected at LEP2. If deviations from the
standard model predictions are observed at LEP2, most likely these are not due
to an underlying supersymmetric structure. In cases where $M_{1/2} \ll A_0,m_0
$, the charginos and neutralinos may give substantial contributions saturating
the LEP2 sensitivity limits. This occurs when their masses $m_{\tilde
C},m_{\tilde Z}$ turn out to be both light satisfying $m_{\tilde C}+m_{\tilde
Z} \simeq M_W $. However these extreme cases are perturbatively untrustworthy
and besides unnatural for they occupy a small region in the parameter space. }
