Isolated Photon Production in Deep Inelastic Compton Process at HERA

The next-to-leading QCD calculation for the isolated photon and isolated photon plus jet photoproduction at the ep collider DESY HERA is presented. The theoretical uncertainties are discussed in details. The predictions are compared with predictions of other authors and with data. The sensitivity of the leading order cross section to the gluon density in both the real and the virtual photon is discussed as well.