Jet cross sections in deeply inelastic scattering at HERA

We present results for (1+1), (2+1) and (3+1)-jet cross sections in deeply inelastic scattering at HERA. We discuss jet definitions at eP-colliders and describe a jet algorithm which takes into account the target jet in the jet analysis. The Born terms for (1+1), (2+1) and (3+1)-jet production were implemented into the weighted Monte-Carlo program PROJET2.2. The numerical calculations yielded a total (3+1)-jet rate of less than 1% for acceptance cuts appropriate for HERA detectors. We show that this small rate can be enhanced considerably by selecting the high-xB region. In addition, we have included the matrix elements for the production of (3+1)-jets in the event generator LEPTO5.2. (orig.)