We present a generalization of the coherent-potential approximation which allows one to describe the average propagation in a disordered medium in which the on-site potential fluctuates in time according to a Markov process. This method appears useful to discuss the dynamics of some manybody problems. By extending the Kubo treatment of the motional narrowing, the averages over histories are performed with use of projection techniques which rely on the augmented-space formalism. Both the binary noise and the Gauss-Markov noise are treated. The one-particle and two-particle average Green functions are derived in each case.