SAR clutter may be characterized by its single-point statistics. Many statistical models for SAR clutter have been proposed in the literature, including the Weibull, log- normal and K distributions, which fit the single point clutter statistics to varying degrees. However, a common feature of all these models is that it is difficult to incorporate correlations into the formulation in an analytically tractable manner. In practice, the only distribution whose multivariate form can be manipulated with any degree of ease is the Gaussian but this distribution does not fit SAR clutter intensities. However, on taking the log of the intensities, the clutter distribution can be approximated by a Gaussian, hence producing the log-normal model. Furthermore, closer approximations can be obtained by using Gaussian mixtures in which a weighted combination of different Gaussians is formed. Correlations may be introduced into this model via the Gaussian components of the mixture distribution. In addition, the weights used in the mixture form a discrete random process upon which correlations may be imposed. The weight process may thus be viewed as a Markov random field which modulates a correlated Gaussian field in the most general formulation. The proposed clutter model is thus an example of a hidden Markov model whose properties will be discussed in this paper.