This paper discusses the applications of dynamic circuit theory to electrodynamic suspension EDS systems. In particular, the paper focuses on the loop-shaped coil and the figure-eight-shaped null-flux coil suspension systems. Mathematical models, including very general force expressions that can be used for the development of computer codes, are provided for each of these suspension systems. General applications and advantages of the dynamic circuit model are summarized. The paper emphasizes the transient and dynamic analysis and computer simulation of maglev systems. In general, the method discussed here can be applied to many EDS maglev design concepts. It is also suited for the computation of the performance of maglev propulsion systems. Numerical examples are presented in the paper to demonstrate the capability of the model.