A general formula is presented that expresses the temporal evolution of compound systems. It connects the time dependence of the density matrix with the energy dependence of the scattering matrix. Using results of random matrix theory, we then study the decay behavior of stochastic compound systems with arbitrary coupling between bound states and decay channels. As an example we consider the case of one open channel and prove a nonexponential decay law for all times that asymptotically is of the form t-3/2.