We systematically analyze the anomalous dipole DELTAk(gamma) and quadr
upole DELTAQ(gamma) moments of the W gauge bosons in the context of th
e minimal supersymmetric standard model as functions of the soft SUSY
breaking parameters A0, m0, M1/2 and the top quark mass. The severe co
nstraints imposed by the radiative breaking mechanism of the electrowe
ak symmetry SU(2) X U(1) are duly taken into account. The supersymmetr
ic values of DELTAk(gamma) and DELTAQ(gamma) can be largely different,
in some cases, from the standard model predictions but of the same or
der of magnitude for values of A0, m0, M1/2 less-than-or-equal-to O(1
TeV). Therefore possible supersymmetric structure can be probed provid
ed the accuracy of measurements for DELTAk(gamma), DELTAQ(gamma) reach
es 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 M1/2 much less than A0, m0, the charginos and neutralinos may gi
ve substantial contributions saturating the LEP2 sensitivity limits. T
his occurs when their masses m(C), m(Z) turn out to be both light sati
sfying m(C) + m(Z) congruent-to M(W). However these extreme cases are
perturbatively untrustworthy and besides unnatural for they occupy a s
mall region in the parameter space,