This paper considers the problem of obtaining efficient estimates for the parameters of a system ofMregression equations. The disturbance terms of this system are assumed to be related by both serial and contemporaneous correlation. Under the further assumption that the serial correlation is a first order autoregressive process, the paper develops an estimator that is consistent and has the same asymptotic normal distribution as the Aitken estimator which assumes the covariance matrix to be known. The paper concludes with a discussion of some alternative covariance specifications and points out certain difficulties with the standard single equation procedures for handling auto-regressive schemes.