  First inclusive measurements of isolated prompt photons in photoproduction at
the HERA ep collider have been made with the ZEUS detector, using an integrated
luminosity of 38.4 pb$^{-1}$. Cross sections are given as a function of the
pseudorapidity and the transverse energy ($\eta^\gamma$, \eTg) of the photon,
for $\eTg > $ 5 GeV in the $\gamma p$ centre-of-mass energy range 134-285 GeV.
Comparisons are made with predictions from Monte Carlo models having
leading-logarithm parton showers, and with next-to-leading-order QCD
calculations, using currently available parameterisations of the photon
structure. For forward $\eta^\gamma$ (proton direction) good agreement is
found, but in the rear direction all predictions fall below the data.
