  The production of prompt photons is measured in the photoproduction regime of
electron-proton scattering at HERA. The analysis is based on a data sample
corresponding to a total integrated luminosity of 340 pb^-1 collected by the H1
experiment. Cross sections are measured for photons with transverse momentum
and pseudorapidity in the range 6 < Et < 15 GeV and -1.0 < eta < 2.4,
respectively. Cross sections for events with an additional jet are measured as
a function of the transverse energy and pseudorapidity of the jet, and as a
function of the fractional momenta x_gamma and x_p carried by the partons
entering the hard scattering process. The correlation between the photon and
the jet is also studied. The results are compared with QCD predictions based on
the collinear and on the k_T factorisation approaches.
