A simple form of measurement error model for explanatory variables is studied incorporating classical and Berkson cases as particular forms, and allowing for either additive or multiplicative errors. The work is motivated by epidemiological problems, and therefore consideration is given not only to continuous response variables but also to logistic regression models. The possibility that different individuals in a study have errors of different types is also considered. The relatively simple estimation procedures proposed for use with cohort data and case-control data are checked by simulation, under the assumption of various error structures. The results show that even in situations where conventional analysis yields slope estimates that are on average attenuated by a factor of approximately 50 per cent, estimates obtained using the proposed amended likelihood functions are within 5 per cent of their true values. The work was carried out to provide a method for the analysis of lung cancer risk following residential radon exposure, but it should be applicable to a wide variety of situations.