  We calculate the QED and QCD radiative corrections to the charged lepton
energy distributions in the dominant semileptonic decays of the top quark $t
\to b W^+ \to b(\ell^+ \nu_\ell)$ $(\ell=e, \mu, \tau)$ in the standard
model(SM), and for the decay $t \to b H^+ \to b(\tau^+ \nu_\tau)$ in an
extension of the SM having a charged Higgs boson $H^\pm$ with $m_{H^\pm} < m_t
-m_b$. The QCD corrections are calculated in the leading and next-to-leading
logarithmic approximations, but the QED corrections are considered in the
leading logarithmic approximation only. These corrections are numerically
important for precisely testing the universality of the charged current weak
interactions in $t$-quark decays. As the $\tau^+$ leptons arising from the
decays $W^+ \to \tau^+ \nu_\tau$ and $H^+\to \tau^+ \nu_\tau$ are predominantly
left- and right-polarised, respectively, influencing the energy distributions
of the decay products in the subsequent decays of the $\tau^+$, we work out the
effect of the radiative corrections on such distributions in the dominant
(one-charged prong) decay channels
  $ \tau^+ \to \pi^+ \bar{\nu}_\tau, \rho^+ \bar{\nu}_\tau, a_1^+
\bar{\nu}_\tau$ and $\ell^+ \nu_\ell \bar{\nu}_\tau$. The inclusive $\pi^+$
energy spectra in the decay chains $t \to b(W^+,H^+) \to b (\tau^+ \nu_\tau)
\to b (\pi^+ \bar{\nu}_\tau \nu_\tau +X)$ are calculated, which can help in
searching for the induced $H^\pm$ effects at the Tevatron and the LHC.
