In this paper we consider a number of estimators for the linear structural simultaneous equations model containing lagged endogenous variables and autocorrelated errors. The special case is considered in which the matrix of autocorrelation coefficients of the (vector) structural error process is diagonal. We consider the two stage least squares analogue (C2SLA) in this case, its relation to the estimators proposed earlier by Fair, the estimator obtained when the autocorrelation matrix is known, and a number of instrumental variables estimators, as well as a modification of the method of scoring which yields an estimator that is asymptotically equivalent to the C2SLA estimator. The asymptotic distributions of such estimators are obtained and we determine their relative asymptotic efficiencies.