  We present theoretical analysis of paired $B_c$ mesons production in $e^+e^-$
annihilation at different energy scales taking into account full
next-to-leading order QCD corrections. Both possible electroweak channels are
considered: production via virtual photon and via virtual $Z$-boson. We study
in detail the role of radiative QCD corrections, which were found to be
significant especially at low energies. It is shown that the contribution from
$Z$-boson is significant at high energies ($\sqrt{s} > M_Z/2$) especially in
the case of paired production of pseudo-scalar and vector ($B_c + B_c^*$)
mesons. Azimuthal asymmetry induced by a $P$-violating weak interaction with
$Z$-boson is also analyzed.
