  The photoproduction of prompt photons, together with an accompanying jet, has
been studied in ep collisions at a centre-of-mass energy of 318 GeV with the
ZEUS detector at HERA using an integrated luminosity of 77 pb-1. Cross sections
were measured for the transverse energy of the photon and the jet larger than 5
and 6 GeV, respectively. The differential gamma+jet cross sections were
reconstructed as functions of the transverse energy, pseudorapidity and
x_gamma^obs, the fraction of the incoming photon momentum taken by the
photon-jet system. Predictions based on leading-logarithm parton-shower Monte
Carlo models and next-to-leading-order (NLO) QCD generally underestimate the
cross sections for the transverse energies of prompt photons below 7 GeV, while
the kT-factorisation QCD calculation agrees with the data better. When the
minimum transverse energy of prompt photons is increased to 7 GeV, both NLO QCD
and the kT-factorisation calculations are in good agreement with the data.
