Measurement of high transverse-energy dijet photoproduction with ZEUS at HERA The cross section for high-ET dijet production in photoproduction was measured with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb-1. The events were required to have a virtuality of the incoming photon, Q2, of less than 1 GeV2 and a photon-proton centre-of-mass energy in the range 142 < W < 293 GeV. Events were selected if at least two jets satisfied the transverse-energy requirements of ET(jet1) > 20 GeV and ET(jet2) > 15 GeV and pseudorapidity requirements of -1 < eta(jet1,2) < 3, with at least one of the jets satisfying -1 < eta(jet) < 2.5. The measurements show sensitivity to the parton distributions in the photon and proton and effects beyond next-to-leading order in QCD. Hence these data can be used to constrain further the parton densities in the proton and photon.