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Complete next-to leading order QCD predictions for (2+1) jet cross sections and jet rates in deep inelastic scattering (DIS) based on a new parton level Monte Carlo program are presented. All relevant helicity contributions to the total cross section are included. Results on total jet cross sections as well as differential distributions in the basic kinematical variables x, W 2 and Q 2 are shown for HERA energies and for the fixed target experiment E665 at FERMILAB. We study the dependence on the choices of the renormalization scale µ R and the factorization scale µ F and show that the NLO results are much less sensitive to the variation of µ = µ F = µ R than the LO results. The effect of an additional p T cut to our jet definition scheme is investigated. * Much higher effective luminosity will be achieved for low Q 2 quasi-real photoproduction of jets. The theoretical interpretation of these events, however, is more difficult, since there is added complication of the direct and the resolved photon contribution to the cross section, which are hard to separate † An extreme example would be (2+1) jet production at very low Q 2 (Q 2 ≈ 1GeV 2 ),where Q 2 cannot be the relevant scale for high p T jet production.

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