The total and differential cross sections for the production of Xi(bc)
', Xi(bc)(()), and Xi(cc)((*)) baryons in gluonic collisions are calc
ulated. The production of the doubly heavy (bc) and (cc) diquarks is c
onsidered in the leading order in alpha(s). It is shown that, for both
low and high transverse momenta of the baryons, the use of the mechan
ism of the heavy-quark fragmentation into a heavy diquark leads to the
cross-section values that are small than the exact numerical results
obtained by evaluating the complete set of diagrams. The yields of bar
yons and antibaryons involving two heavy quarks are estimated for the
Tevatron experiments. The results are (1.3 +/- 0.3) x 10(5) bcq baryon
s and (1.6 +/- 0.3) x 10(4) ccq baryons at p(T) > 5 GeV and /y/ < 1 wi
th allowance for antiparticle production.