The asymmetries ${cal A}_k equiv [Gamma(twddec) -Gamma(tbwddec)] /[Gamma(twddec) + Gamma(tbwddec)]$ 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 the 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 ${cal A}_b$ can be substantial, ${cal O}(alpha_{QCD})$, provided the CP-violating phase of gluino-top-stop couplings is not suppressed. Within the SSM ${cal A}_b$ is generated by the vertex corrections.
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