AbstractIn this paper we present an estimating equation approach to statistical inference for non‐linear random effects regression models for correlated data. With this approach, the distribution of the observations and the random effects need not be specified; only their expectation and covariance structure are required. The variance of the data given the random effects may depend on the conditional expectation. An approximation to the conditional expectation about the fitted value of the random effects is used to obtain closed form expressions for the unconditional mean and covariance of the data. The proposed methods are illustrated using data from a mouse skin painting experiment.