  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 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 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. 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
h_c+\chi_{cJ} at the center-of-mass energy sqrt{s}=10.6 GeV.
