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We have calculated inclusive two-jet cross sections in next-to-leading orderQCD for direct photoproduction in low $Q^2$ $ep$ collisions at HERA. Infraredand collinear singularities in real and virtual contributions are cancelledwith the phase space slicing method. Analytical formulas for the differentcontributions giving the dependence on the slicing parameter are presented.Various one- and two-jet distributions have been computed demonstrating theflexibility of the method.Comment: 30 pages, latex, 11 figures appended as uuencoded fil

Inclusive dijet production at HERA: direct photon cross sections in next-to-leading order QCD