  In the framework of QCD perturbation theory, total and differential cross
sections of the $\Xi_{bc}'$, $\Xi_{bc}^{(*)}$ and $\Xi_{cc}^{(*)}$ baryons
production in gluon collisions are calculated in the leading order over
$\alpha_s$ for the doubly heavy ($b c$) and ($ c c$) diquarks. At both small
and large transverse momenta of the baryons, a use of the mechanism of the
heavy quark fragmentation into the heavy diquark is shown to underestimate the
cross section values in comparison with the exact numerical calculations of
complete set of diagrams. The expected in Tevatron experiments yield of baryons
with two heavy quarks is evaluated as $(1.3\pm 0.3) \cdot 10^5 \,\,
bcq$-baryons and $(1.6\pm 0.3) \cdot 10^4 \,\, ccq$-baryons at $p_T>5$ GeV and
$|y|<1$ of the baryon momentum and rapidity cuts, with account for the
antiparticle yields.
