  We present the first calculation of inclusive jet photoproduction with
next-to-next-to-leading order (NNLO) contributions, obtained from a unified
threshold resummation formalism. The leading coefficients for direct
photoproduction are computed analytically. Together with the coefficients
pertinent to parton-parton scattering, they are shown to agree with those
appearing in our full next-to-leading order calculations. For hadron-hadron
scattering, numerical agreement is found with a previous calculation of jet
production at the Tevatron. We show that the direct and resolved NNLO
contributions considerably improve the description of final ZEUS data on jet
photoproduction and that the error on the determination of the strong coupling
constant is significantly reduced.
