A polynomial structural errors-in-variables model with normal underlying distributions is investigated. An asymptotic covariance matrix of the SLS estimator is computed, including the correcting terms which appear because in the score function the sample mean and the sample variance are plugged in. The ALS estimator is also considered, which does not need any assumption on the regressor distribution. The asymptotic covariance matrices of the two estimators are compared in border cases of small and of large errors. In both situations it turns out that under the normality assumption SLS is strictly more efficient than ALS.