Jet cross sections in DIS and photoproduction at HERA ZEUS Collaboration Abstract Jet cross sections in deep inelastic ep scattering and photoproduction were measured with the ZEUS detector at HERA using an integrated luminosity of up to 500 pb^-1. Measurements of differential cross sections are presented for inclusive-jet and dijet production and compared with perturbative QCD predictions. Regions of phase space where the cross sections are sensitive to the gluon content of the proton with small uncertainties were identified. These measurements have the potential to constrain the gluon density in the proton when included as input to global QCD fits. A QCD analysis of the measured cross sections was also used to extract precise values of the strong coupling and test its energy-scale dependence.