Decomposition and stability of multifronts and multipulses In this thesis we consider time dependent reaction diffusion systems in one space dimension that have multiple pulse or front solutions. We develop a new numerical method that decomposes the solutions into their single pulses or fronts and in addition one computes the speeds and the positions of the single pulses and fronts. We show that the method is numerically feasible and prove stability results for the multiple pulse and front solutions if the distance of the pulses or fronts is sufficiently large and they interact only through their small tails.