An initial value problem for one_dimensional wave propagation is considered; the medium is assumed to be randomly perturbed as a function of both space and time. The stochastic perturbation theory of Papanicolaou and Keller [SIAM J. Appl. Math. 21, 287 (1971)] is applied directly in the space-time regime to derive transport equations for the first and second moments of the solution. These equations are solved in special cases.