  The precision of new HERA data on jet photoproduction opens up the
possibility to discriminate between different models of the photon structure.
This requires equally precise theoretical predictions from perturbative QCD
calculations. In the past years, next-to-leading order calculations for the
photoproduction of jets at HERA have become available. Using the kinematic cuts
of recent ZEUS analyses, we compare the predictions of three calculations for
different dijet and three-jet distributions. We find that in general all three
calculations agree within the statistical accuracy of the Monte Carlo
integration yielding reliable theoretical predictions. In certain restricted
regions of phase space, the calculations differ by up to 5%.
