This thesis is concerned with the steady-state analysis' of the brush less doubly-fed machine ( BDFM ). The first part of the thesis is dedicated to the derivation of an analytical model based on generalised harmonic analysis. The model allows for any combination of pole numbers in the stator windings and can readily access the effect of stator space harmonics. The most usual rotor configurations can be accommodated and the rotor currents can be examined. In addition, the harmonic analysis identifies: the role of the rotor slot harmonics in facilitating the interaction between the stator fields; rotor requirements for synchronous operation and limitations on the combination of pole numbers in the stator windings. The model is validated using a prototype machine built at the University of Cambridge and gives very good predictions for the machine performance when operating at low saturation levels. The results show that the machine presents a closely linear relationship between the input power and the load torque, similar to that of a synchronous machine. In addition, the power factor can be controlled by the converter voltage. Theoretical studies ratify that the machine can be controlled using a converter that only needs to handle a percentage of the total input power and identify the relationship between the direction of power flow in the converter and the natural speed of the machine. This is particularly useful when designing a machine that can be used with a uni-directional converter. The second part of the thesis is concerned with the development of a model based on the Finite Element Method. Broadly, the machine is modelled using circuit equations and the finite element analysis is used to up-date the circuit inductances. The finite element model is also validated against the prototype machine and is shown to produce very good results. It is also used to investigate the field distribution in the BDFM and to calculate iron loss.