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Autoregressive-Moving Average (ARMA) dynamic models of two-dimensional bistationary processes are obtained and used to clarify the problem of optimum, recursive, spatially causal estimation of such processes. Two specific methods for the realization of optimum or suboptimum estimators are examined. The first is based on a general dynamic model of two-dimensional processes, identifiable via a variant of the Yule-Walker equations used for the identification of stationary time series. This method is computationally tractable. The second leads to a novel and as yet unsolved factorization problem for bivariate spectra.