  In the framework of the kt-factorization approach, the production of prompt
photons in association with a heavy (charm or beauty) quarks at high energies
is studied. The consideration is based on the O(\alpha \alpha_s^2) off-shell
amplitudes of gluon-gluon fusion and quark-(anti)quark interaction
subprocesses. The unintegrated parton densities in a proton are determined
using the Kimber-Martin-Ryskin prescription. The analysis covers the total and
differential cross sections and extends to specific angular correlations
between the produced prompt photons and muons originating from the semileptonic
decays of associated heavy quarks. Theoretical uncertainties of our evaluations
are studied and comparison with the results of standard NLO pQCD calculations
is performed. Our numerical predictions are compared with the recent
experimental data taken by the D0 and CDF collaborations at the Tevatron.
Finally, we extend our results to LHC energies.
