[en] We have calculated the next-to-leading order cross sections for the inclusive production of D^*-mesons in ep collisions at HERA for finite, although very small Q². In this Q²-range, the same approximations as for photoproduction can be used. Our calculation is performed in the general-mass variable-flavour-number scheme. In this approach, large logarithms of the charm transverse momentum are resummed and finite terms depending on m²/p_T² are kept in the hard scattering cross sections. The theoretical results are compared with recent data from the ZEUS collaboration at HERA. On average, we find good agreement. (orig.)