This paper presents a systematic study of the various control loops in a current source inverter-induction motor drive and their effects on the dynamic response and stability of the system. A dq model is developed which incorporated the induction motor and the inverter power supply with current feedback. The model is first used to generate steady-state curves to determine operating points. A linearized small signal model is developed to study stability and provide transfer functions for various control strategies. The stabilizing effect of adding first slip speed control and then flux control is investigated. Two possible implementations of the flux control are compared, showing insignificant difference. The study reveals that with flux control, several pole-zero cancellations are possible, thereby simplifying the model and the design of other outer control loops such as speed or torque.