In the present project parametric instabilities in laser-produced plasmas will be investigated theoretically. Of particular interest will be stimulated Brillouin scattering (SBS) and its interplay with filamentation of the laser beam. SBS causes reflection of the incident laser light. For laser fusion it is therefore a loss mechanism of energy for heating the plasma by light absorption whereas filamentation of the incident beam destroys the uniformity of the energy deposit. The saturation of SBS, seen in many experiments is still poorly understood and will be studied in detail for long scale-length plasmas using advanced numerical and analytical models. The coupling between SBS and filamentation will be investigated in two- and three-dimensional geometry. A newly developed code will be used which allows to understand the interplay between both mechanisms and will yield explanation and predictions for experiments.