  The production of the charmonium states in hadronic experiments is considered
in NLO at the strong coupling constant. It is shown, that such an approach
solves some significant problems, arising when only leading order processes are
considered. In particular, in such a consideration distributions over the
transverse momentum of the final charmonium can be obtained. There appears also
a natural explanation to the existence of $\chi_{c1}$-meson in final state,
that is observed experimentally and cannot be produced in leading order
processes.
