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This paper studies wave propagation through a deep phase screen in which the properties vary randomly both with time and space. Two approaches will be discussed. One is analytical, the other involves numerical simulation. In the analytical approach, asymptotic expressions for the space-time correlation functions of the wave field are derived for the case of gaussian random irregularities. For the simulation approach, general prescribed space-time random variations of irregularities are generated and used to represent a time varying phase screen. This technique can be used to model a screen with a power-law type of irregularity spectrum. Numerical propagation code is then used to compute the wave fields at the reception plane from which statistics will be calculated. The relations between the statistics of the wave fields and the space-time variations of the medium will be discussed. Applications of the results will be discussed.