Measurements of heavy-quark production at HERA constrain the structure of the proton, and have provided valuable indications of perturbative QCD. In this publication measurements of heavy-flavour jet cross sections in photoproduction and deep inelastic scattering (DIS), performed by the H1 and ZEUS collaborations, are presented using inclusive techniques for the signal extraction. The results are compared to next-to-leading order QCD calculations and found to be in reasonable agreement with theory predictions.