  We compute total cross sections for charm and bottom photoproduction at HERA
energies, and discuss the relevant theoretical uncertainties. In particular we
discuss the problems arising from the small-$x$ region, the uncertainties in
the gluon parton density, and the uncertainties in the hadronic component of
the cross section. Total electroproduction cross sections, calculated in the
Weizs\"acker-Williams approximation, are also given.
