  The semileptonic B_c-meson decays into the heavy quarkonia J/\psi (\eta_c)
and a pair of leptons are investigated in the framework of three-point sum
rules of QCD and NRQCD. Calculations of analytical expressions for the spectral
densities of QCD and NRQCD correlators with account for the Coulomb-like
\alpha_s/v terms are presented. The generalized relations due to the spin
symmetry of NRQCD for the form factors of B_c\to J/\psi (\eta_c)l\nu_l
transitions with l denoting one of the leptons e, \mu or \tau, are derived at
the recoil momentum close to zero. This allows one to express all NRQCD form
factors through a single universal quantity, an analogue of Isgur-Wise function
at the maximal invariant mass of lepton pair. The gluon condensate corrections
to three-point functions are calculated both in full QCD in the Borel transform
scheme and in NRQCD in the moment scheme. This enlarges the parameteric
stability region of sum rule method, that makes the results of the approach to
be more reliable. Numerical estimates of widths for the transitions of B_c\to
J/\psi (\eta_c)l\nu_l are presented.
