  Recent ZEUS measurements of inclusive-jet and dijet cross sections in neutral
current deep inelastic ep scattering at HERA are presented. The data correspond
to more than a two-fold increase in statistics compared to previous studies.
The cross sections are measured in the Breit frame, for boson virtualities of
Q^2 > 125 GeV^2, as functions of various kinematic and jet observables. The
data are found to be well described by NLO QCD and have the potential to
constrain the gluon density in the proton. Two new extractions of the strong
coupling, alpha_s, are also presented: the first is determined from the
inclusive-jet neutral current DIS measurement presented here, while the second
is from a re-analysis of previously published data on inclusive jet
photoproduction. Both measurements are of competitive precision and in
agreement with the world average.
