Summary: This paper advocates likelihood analysis for regression models with measurement errors in explanatory variables, for data problems in which the relevant distributions can be adequately modelled. Although computationally difficult, maximum likelihood estimates are more efficient than those based on first and second moment assumptions, and likelihood ratio inferences can be substantially better than those based on asymptotic normality of estimates. The EM algorithm is presented as a straightforward approach for likelihood analysis of normal linear regression with normal explanatory variables, and normal replicate measurements.