We show how an estimator obtained for maximizing an incorrect working likelihood can be adjusted to remove its asymptotic bias. The resulting estimator is called an adjusted quasi maximum likelihood estimator (AQMLE). Asymptotic properties of the AQMLE are derived, and its efficiency is shown to be directly related to the square of the correlation between the score functions for the working and true likelihoods. The adjustment is made by solving a set of equations obtained from the expectation of the working likelihood score function with respect to the true model. We consider extensions to cases where the true likelihood is not completely specified, and equations giving the asymptotic bias adjustment are based on an estimate of the true cdf. Applications to other types of estimating equations are briefly reviewed. Key words: Asymptotic bias adjustment, biased estimating equations, incorrect likelihoods.