  The presented paper is devoted to theoretical analysis of charmonium mesons
$\eta_c$, $J/\psi$, $\chi_{c0,1,2}$, and $h_c$ production in exclusive
radiative $Z$ boson decays in the frameworks of Nonrelativistic Chromodynamic
and amplitude expansion on the light-cone. In the framework of light-cone
expansion amplitudes and widths of all processes are described with one
universal relation. It is interesting to note that from this relation it
follows automatically which component of $Z$ boson (either vector or axial)
gives contribution to the width of the particular decay. It is shown that the
effect of internal quark motion almost doubles theoretical predictions for
production of $S$-wave charmonia and $\chi_{c1}$ meson.
