Summary. A dynamic regime is a function that takes treatment and covariate history and baseline covariates as inputs and returns a decision to be made. Murphy (2003, Journal of the Royal Statistical Society, Series B65, 331–366) and Robins (2004, Proceedings of the Second Seattle Symposium on Biostatistics, 189–326) have proposed models and developed semiparametric methods for making inference about the optimal regime in a multi-interval trial that provide clear advantages over traditional parametric approaches. We show that Murphy's model is a special case of Robins's and that the methods are closely related but not equivalent. Interesting features of the methods are highlighted using the Multicenter AIDS Cohort Study and through simulation.