A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency (but not in the sort of drug) a reasonable assumption is that the regression models for the different treatments share common parameters. During the talk we develop optimal design theory for the comparison of different regression models with common parameters. We derive upper bounds on the number of support points of admissible designs, and explicit expressions for D-optimal designs for frequently used dose response models with a common location parameter. If the location and scale parameter in the different models coincide, the problem becomes much harder and therefore we determine minimally supported designs and sufficient conditions for their optimality in the class of all designs.