SUMMARY General aspects of nonlinearity in the context of component of variance models are discussed, and two special topics are examined in detail. Firstly, simple procedures, both formal and informal, are proposed for describing departures from normal-theory linear models. Transformation models are shown to be a special case of a more general formulation, and data on blood pressure are analyzed in illustration. Secondly, an approximate likelihood is proposed and its accurate performance is examined numerically using examples of exponential regression and the analysis of several related 2 x 2 tables. In the latter example, the approximate score test has improved power over the MantelHaenszel test.