  The MSSM predictions at the one-loop level for the weak dipole moments of the
\tau lepton and the b quark are presented. The imaginary part of the AWMDM is
of the order of the SM contribution whereas the real part may be a factor 5
(20) larger for the \tau (b) in the high \tan\beta scenario, still a factor
five below the QCD contribution in the b case. More interestingly, a
contribution up to twelve orders of magnitude larger than in the SM may be
obtained, already at the one-loop level, for the WEDM in a MSSM with complex
parameters.
