Jet cross sections and extraction of alphas at HERA ZEUS Collaboration Abstract Jet cross sections in deep inelastic ep scattering (DIS) 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 production in DIS and photoproduction and the trijet to dijet ratio in DIS and compared with perturbative QCD predictions. A QCD analysis of the measured observables was used to extract precise values of the strong coupling and test its energy-scale dependence.