  On the basis of perturbative QCD and the relativistic quark model we
calculate relativistic and bound state corrections in the production processes
of a pair of S-wave and P-wave charmonium states. Relativistic factors in the
production amplitude connected with the relative motion of heavy quarks and the
transformation law of the bound state wave function to the reference frame of
the moving S- and P-wave mesons are taken into account. For the gluon and quark
propagators entering the production vertex function we use a truncated
expansion in the ratio of the relative quark momenta to the center-of-mass
energy $\sqrt{s}$ up to the second order. The exact relativistic treatment of
the wave functions makes all such second order terms convergent, thus allowing
the reliable calculation of their contributions to the production cross
section. Relativistic corrections to the quark bound state wave functions in
the rest frame are considered by means of the Breit-like potential. It turns
out that the examined effects change essentially the nonrelativistic results of
the cross section for the reaction $e^++e^-\to J/\Psi(\eta_c)+\chi_{cJ}(h_c)$
at the center-of-mass energy $\sqrt{s}=10.6$ GeV.
