Total Cross Sections for Heavy Flavour Production at HERA

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.