This paper deals with the steady-state investigation of a doubly-fed asynchronous machine (DFAM) supplied by a current controlled cycloconverter (CCC) in the rotor, and an a.c. mains in the stator. The model of the DFAM is based on a space vector representation. The theoretical analysis, then the characteristics at constant torque are presented. The DFAM is shown to behave like a non-salient synchronous machine, and the excitating and stator currents are homologous in both machines. This analogy is confirmed by the stator-rotor current characteristics at constant torque and the reactive power flow in the DFAM. The transient performances and the dynamic stability are analysed too. The simplification of the transfer function of the system allows to the same stability condition for any perturbation.