  The effect of lepton transverse polarization in the B^0 --> D^- l^+ nu_l, B^+
--> bar(D^0) l^+ nu_l decays (l= tau, mu) is analyzed within the framework of
Standard Model in the leading order of HQET. It is shown that the non-zero
transverse polarization appears due to the electromagnetic final state
interaction. The diagrams with intermediate D, D^* - mesons contributing to the
non-vanishing P_T are considered. Regarding only the contribution of these
mesons, values of the tau-lepton transverse polarization, averaged over the
physical region, in the B^0 --> D^- tau^+ nu_l and B^+ --> bar(D^0) tau^+ nu_l
decays are equal to $2.60 cdot 10^{-3} and -1.59 cdot 10^{-3}, correspondingly.
In the case of muon decay modes the values of <P_T> are equal to 2.97 cdot
10^{-4} and -6.79 cdot 10^{-4}.
