SUMMARY The paper analyses a simultaneous linear model representing stationary spatial-temporal processes. For processes with unit spatial orders, a simple method to compute the likelihood function is developed. Unfortunately, this technique does not generalize to higher order processes. Alternative methods applicable to higher order processes are developed. Finally, it is shown how predictions can be made over time if the parameters are known. Whittle (1954) analysed a simultaneous linear spatial model and discussed likelihood inference for its unknown parameters. The major difficulty in analysing such a model is to evaluate a Jacobian which arises because of the multilateral nature of the process, i.e. because the random variable at a location depends on the random variables at the locations around it. Whittle developed an ingenious method for approximating this determinant. Ord (1975) treated a special case of the simultaneous model with one parameter defined on irregular lattices and showed an exact method for computing the relevant determinant. In ? 2, we generalize Whittle's two-dimensional spatial model to formulate a spatialtemporal model and derive the likelihood function from a single realization on finite rectangular lattices over time. Section 3 analyses spatial-temporal models with unit spatial orders, where the Jacobian has been put into a simple computational form. Section 4 develops alternative methods for computation of the Jacobian applicable to higher-order processes. We take up the prediction aspect of the model in ? 5.