The crossover design is a type of longitudinal study with subjects receiving different treatments in different time periods. When carry-over effects are absent, the usual crossover design is structured so that all the information about treatment effects is contained in the within-subject contrasts; standard analyses are based on these within-subject contrasts and ignore any between-subject information. With carry-over effects present these standard analyses can be very inefficient, especially for suboptimal designs. We describe alternative approaches based on methods for the analysis of longitudinal data.