  Exclusive semileptonic decays of B mesons to orbitally excited D mesons are
considered beyond the infinitely heavy quark limit in the framework of the
relativistic quark model based on the quasipotential approach. This model
agrees with the structure of heavy quark mass corrections predicted by the
heavy quark effective theory and allows the determination of corresponding
leading and subleading Isgur-Wise functions. It is found that both relativistic
and 1/m_Q contributions significantly influence the decay rates. Thus,
relativistic transformations of the meson wave functions (Wigner rotation of
the light quark spin) already contribute at leading order of the heavy quark
expansion and result in a suppression of B\to D^{*}_0e\nu and B\to D^{*}_1e\nu
decay rates. On the other hand, the vanishing of the decay matrix elements at
zero recoil of a final D^{**} meson in the infinitely heavy quark mass limit
makes the 1/m_Q corrections to be very important, and their account results in
a substantial enhancement of B\to D_1e\nu and B\to D^{*}_0e\nu decay rates.
