In this paper we present a mathematical analysis of the four classical indirect response models. We focus on characteristics such as the evolution of the response R(t) with time t, the time of maximal/minimal response T max and the area between the response and the baseline AU C R , and the way these quantities depend on the drug dose, the dynamic parameters such as E max and EC 50 and the ratio of the fractional turnover rate k out to the elimination rate constant k of drug in plasma. We find that depending on the model and on the drug mechanism function, T max may increase, decrease, decrease and then increase, or stay the same, as the drug dose is increased. This has important implications for using the shift in T max as a diagnostic tool in the selection of an appropriate model.