The production of high $P_T$ hadronic jets is discussed using Quantum-Chromodynamic pertubation theory. Predictions are given for both single jet and two jet cross-sections and effects due to the transverse motion of the interacting partons are discussed. Not only quark-quark scattering but all contribution in lowest order are considered. At low $X_r$, gluon-gluon and gluon-quark scattering are founded to dominate the quark-quark term.