Isolated-photon production in ep collisions at HERA ZEUS Collaboration Abstract Isolated-photon production has been measured in ep collisions at a centre-of-mass energy of 318 GeV with the ZEUS detector at HERA using an integrated luminosity of 320 pb-1. Measurements of inclusive prompt-photon cross sections are presented as functions of the photon transverse energy and pseudorapidity in a wide range of exchanged-photon virtuality. In addition, differential gamma+jet cross sections are presented as functions of the jet transverse energy and pseudorapidity. Leading-logarithm parton-shower Monte Carlo predictions and perturbative QCD calculations are compared to the data.