  Calculations of the hadronic $B^{(*)}_c$-mesons production performed in the
framework of the perturbative QCD taking into account $O(\alpha_s^4)$ Feynmann
diagrams are presented. A comparison of the exact calculations with those based
on the fragmentation model of $\bar b\rightarrow B^{(*)}_c+X$ shows the large
discrepancy between them. The exact calculations of the $B^{(*)}_c$-mesons
production cross-sections as the function of $p_T$ at the energy of the FNAL
Tevatron ($\sqrt{s}=1.8$ TeV) are given. The predicted ratio of the vector to
the pseudoscalar state cross-sections is about $R\sim 3$ instead of $R\sim 1.4$
for the fragmentation model.
