  The cross section values of $J/\psi\ \eta_c$ and $J/\psi\ J/\psi$ production
in $e^+e^-$ annihilation are estimated within one-loop approximation near $Z$
pole, as well as at higher energies. Both intermediate bosons, $\gamma$ and
$Z$, are taken into account. It is shown that at $Z$ mass the NLO contribution
increases the cross-section values by 3.5 times.
