  We consider the prompt photon production at high energy hadron colliders in
the framework of k_T-factorization approach. The unintegrated quark and gluon
distributions in a proton are determined using the Kimber-Martin-Ryskin
prescription. The conservative error analisys is performed. We investigate both
inclusive prompt photon and prompt photon and associated muon production rates.
In Standard Model such events come mainly due to Compton scattering process
where the final heavy (charm or bottom) quark produces a muon. The theoretical
results are compared with recent experimental data taken by the D0 and CDF
collaborations at Fermilab Tevatron. Our analysis also covers the azimuthal
correlations between produced prompt photon and muon which can provide an
important information about non-collinear parton evolution in a proton.
Finally, we extrapolate the theoretical predictions to CERN LHC energies.
