This paper deals with longitudinal motion control of electric vehicles (EVs) driven by in-wheel-motors (IWMs). It shows that the IWM-EV is fundamentally a multi-agent system with physical interaction. Three ways to model the IWM-EV are proposed, and each is applicable to certain control objectives. Firstly, a nonlinear model with hierarchical structure is established, and it can be used for passivity-based motion control. Secondly, a linearized model with rank-1 interconnection matrix is presented for stability analysis. Thirdly, a time-varying state-space model is proposed for optimal control using linear quadratic regulator (LQR). The proposed modellings contribute the new understanding of IWM-EV dynamics from the view point of multi-agent-system theory. By choosing the suitable control theory for each model, the complexity level of system design is maintained constant, no matter what the number of IWMs installed to the vehicle body. The effectiveness of three models and their design approaches are discussed by several examples with Matlab/Carsim co-simulator.