When the error covariance matrix in a linear model depends on a few unknown parameters, the regression coefficients can be estimated by a two-step procedure. Consistent estimates of the covariance parameters are first obtained and then used in a generalized least squares regression. Under the assumption that the errors are normal and the covariance parameter estimates are well behaved, an asymptotic expansion is developed for the distribution function of the two-step GLS estimate. the error in treating the estimate as normal is found to be of order n^-^2 as the sample size n tends to infinity.