Two possible mechanisms are responsible for the temporal broadening of pulses propagating in a turbulent medium. The ensemble averaged pulse may be broadened owing to the fact that each realization of the ensemble is spread in time as a consequence of scattering. It may also come about because of the wandering of the pulse. In this paper these two mechanisms are studied. First, the two-frequency and the four-frequency mutual coherence functions for the field are obtained for both the Rytov approximation and the asymptotic saturated condition. They are then used to compute the spreading and wandering of the pulse. It is found that under the condition of weak scattering, pulse wandering dominates the contribution to the broadening of the pulse. In the saturated region, however, pulse spreading becomes the dominant factor. Explicit expressions for the spreading and wandering are derived for some examples.