  The next-to-leading order (NLO) QCD calculation for the isolated photon and
isolated photon plus jet photoproduction at the ep collider DESY HERA is
presented. The predictions for the isolated photon with no restrictions imposed
on the jet are compared with the previous ones obtained in the small cone
approximation, and the differences are found to be below 2%. The theoretical
uncertainties in the cross section of the photoproduction of the photon plus
jet are discussed. A short comparison with the new preliminary H1 data and with
the NLO predictions of Fontannaz et al. is also presented.
