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Processes of heavy quark photoproduction at HERA energies and beyond areinvestigated using the semihard ($k_{\bot}$ factorization) approach. Virtualityand longitudinal polarization of gluons in the photon - gluon subprocess aswell as the saturation effects in the gluon distribution function at small $x$have been taken into account. The total cross sections, rapidity and $p_{\bot}$distributions of the charm and beauty quark photoproduction have beencalculated. The results are compared with ZEUS experimental data for charmphotoproduction cross section.Comment: LaTeX, 10 pages, 6 figs not included (available via mail on request

HEAVY QUARK PHOTOPRODUCTION IN THE SEMIHARD APPROACH AT HERA AND BEYOND