  We estimate the differential and total cross sections for both the
photoproduction of vector D*-meson and its yield in deep inelastic scattering
at the HERA collider in the framework of model motivated by perturbative
calculations in QCD. The offered model allows us to take into account higher
twists over the transverse momentum of meson at p_T ~ m_c and to correctly
approach the dominance of $c$-quark fragmentation at p_T >> m_c. We consider a
possibility for the hadronization of color-octet c q-bar state into the meson.
The combined contribution by the singlet and octet-color terms results in a
good agreement with the experimental data for both the photoproduction and the
production in deep inelastic scattering.
