The asymmetries A(k) = [GAMMA(t --> W+d(k))-GAMMA(tBAR --> W-d(k)BAR)]
/[GAMMA(t --> W+d(k))+GAMMA(tBAR --> W-d(k)BAR)] in the partial widths
of the top quark decays are discussed within the Standard Model (SM),
the Two-Higgs-Doublet Model (2HDM) and supersymmetric extensions of t
he SM (SSM). The leading contributions to these asymmetries in the SM
and in the 2HDM are induced by the up-type quark self-energy diagrams
and are found to be very small. However, in the SSM, the asymmetry A(b
) can be substantial, O (alpha(QCD)), provided the CP-violating phase
of gluino-top-stop couplings is not suppressed. Within the SSM A(b) is
generated by the vertex corrections.