[en] Jetproduction in the collision of quasi-real photons with protons at center-of-mass energies between 130 and 270 GeV at HERA is analyzed using data taken by the ZEUS experiment in 1993. General characteristics of jet production are studied. Dijet-events are analyzed, yielding an unambigious signal for both resolved and direct photon processes. Inclusive jet differential cross sections are given for all contributing processes and for photon diffractive dissociation. The study of jet profiles is consistent with the hypothesis of multiple parton interactions in resolved photon processes. (orig.)