We compute various kinematical distributions for one-jet and two-jet inclusive photoproduction at HERA. Our results are accurate to next-to-leading order in QCD. We use the subtraction method for the cancellation of infrared singularities. We perform a thorough study of the reliability of QCD predictions; in particular, we consider the scale dependence of our results and discuss the cases when the perturbative expansion might break down. We also deal with the problem of the experimental definition of the pointlike and hadronic components of the incident photon, and briefly discuss the sensitivity of QCD predictions upon the input parameters of the calculation, like $alpha_S$ and the parton densities.
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