  We discuss the inclusive production of D*+- mesons in gamma-proton collisions
at DESY HERA, based on a calculation at next-to-leading order in the
general-mass variable-flavor-number scheme. In this approach, MSbar subtraction
is applied in such a way that large logarithmic corrections are resummed in
universal parton distribution and fragmentation functions and finite mass terms
are taken into account. We present detailed numerical results for a comparison
with data obtained at HERA and discuss various sources of theoretical
uncertainties.
