  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.
