It has been argued for many years that models used to analyze data from crossover designs are not appropriate when simple carryover effects are assumed. Furthermore, a statistical model that could estimate complex carry-over effects in crossover designs had never been found. However, in this paper, the estimability conditions of the complex carryover effects and a theoretical result that supports them are found. In addition, a simulation example is developed in a non-linear dose-response test for a typical AB/BA crossover design with repeated measures. This simulation shows that a semiparametric model can detect complex carryover effects and that this estimation improves the precision of the estimators of the treatment effect. It is concluded that when there are at least five replicates in each observation period per individual, semiparametric statistical models provide a good estimator of the treatment effect and reduce bias with respect to models that assume the absence of carryover effects or simplex carryover effects. Furthermore, an application of the methodology is shown and the wealth of analysis gained by estimating complex carryover effects is evident.