This paper addresses the effects of simultaneous misclassification of both exposure and disease on epidemiologic measures of association. If misclassification of a dichotomous exposure is independent of a dichotomous disease status and vice versa (non-differential misclassification), and misclassification of exposure is independent of misclassification of disease, then the bias is always toward the null. In practice, however, errors in exposure and disease ascertainment may often be correlated. In this case, the observed exposure-disease association may be strongly biased in any direction even with non-differential misclassification. As an important corollary, the assertion commonly made in the discussion of epidemiologic study results that the observed measures of association can only be biased toward the null due to presumedly non-differential misclassification has to be viewed as inadequate unless the assertion that exposure and disease misclassification are independent is also justified. Inferences regarding the degree and direction of bias due to misclassification of exposure and disease should consider plausible degrees of correlation in classification errors in addition to the overall misclassification rates. Whenever possible, sensitivity analyses should be performed to provide a quantitative basis for such inferences.