Master Thesis: Creating a Hybrid of Matrix Elements and Parton Showers LU TP 97-12 Johan Andre' Abstract: The second-order QCD matrix elements give a very good agreement with experimental data on the angular distributions of the four-jet events in e+e- collisions at the Z0 resonance energy. Unfortunately the description of the sub-jet structure is quite poor. The alternative approach, parton showers, gives a good description of the sub-jet structure but is worse than matrix elements when it comes to the angular distributions. Here is presented a hybrid between the matrix elements and the parton showers that is intended to combine the best of the two approaches.