  The production of charmed and beauty hadrons in proton-proton and
proton-antiproton collisions at high energies is analyzed within the modified
quark-gluon string model (QGSM) including the internal motion of quarks in
colliding hadrons. It is shown that using both the QGSM and NLO QCD one can
describe the experimental data rather successfully in a wide region of
transverse momenta. We also present some predictions for the future experiments
on the beauty baryon production in $pp$ collisions at LHC energies and on the
charmed meson production in ${\bar p}p$ reactions at GSI energies.
