Over the past ten years, considerable attention has been paid to the genetic analysis of binary or ordered polychotomous data. But potential applications of nonlinear models in animal breeding settings go far beyond. Examples are reviewed here. Initially, methods and algorithms for estimating dispersion parameters in nonlinear models were designed as mere extensions of procedures developed for |inear models. Recent work, often resting on Bayesian methodology, has helped to justify and understand the interest and limitations of these methods. Beyond the estimation of dispersion parameters, many problems important to animal breeders and related to the interpretation and the use of these parameters remain to be solved.