Several statistical models have been proposed for the genetic evaluation of production traits in dairy cattle based on test-day records. Three main approaches have been put forward in the literature: random regression, orthogonal polynomials, and, more recently, character process models. The aim of this paper is to show how these different approaches are related, to compare their performance for the genetic analysis of lactation curves, and to assess equivalence between sire and animal models for repeated measures analyses. It was found that, with an animal model, a character process model with 11 parameters performed better, regarding the likelihood criterion, than a quartic random regression model (with 31 parameters). However, although the likelihood was higher, the genetic variance was very different with the character process model from the unstructured model, which raises important issues concerning model selection criteria. There are advantages in combining methodologies. A quadratic random regression model for the environmental part, combined with a character process model for the residual, performed better than the quartic random regression model and had fewer parameters. A character process structure allowing for a correlation pattern modeled the residual better than a simple quadratic variance, and had only one extra parameter.