The Brushless Doubly-Fed Machine (BDFM) shows commercial promise as a variable speed drive or generator. However, for this promise to be realised the design of the machine must be improved beyond that proposed to date. This dissertation contributes towards this goal through machine analysis, design and control. A generalised framework is developed for a coherent and rigorous derivation of models for a wide class of BDFMs, of which machines with 'nested-loop' design rotors are a subset. This framework is used to derive coupled circuit, d-q axis, sequence components and then equivalent circuit models for the class of machines. Proofs are given for all derivations, exploiting the circulant properties of the mutual inductance matrices. The coherence between the different models allows parameters calculated for the coupled circuit model to provide parameter values for the other models. A method of model order reduction is proposed for the class ofBDFMs with 'nested-loop' rotors, and examples given of the efficacy of the procedure. The reduction method allows parameter values to be computed for a simple equivalent circuit representation of the machine. These calculated parameter values, and those for other BDFM rotor designs are verified by experimental tests on a prototype BDFM. The significance of particular equivalent circuit parameters is investigated from the model. Series rotor inductance terms are found to have a significant and direct effect on machine petformance. These terms are shown to relate directly to the design of the rotor, and are quantified using the previously developed framework. Seven different rotor designs, including a new BDFM rotor design, are considered to show how the values of these parameters change. An experimental method of parameter estimation is developed for the equivalent circuit model, and the relationship between these parameters and the parameters in other forms of the model derived. The experimental method is shown to be applicable both to standard induction machines and to BDFM machines, yielding accurate results in each case. A synchronous reference frame model for the class ofBDFMs is derived and is used to analyse the stability of the machine via a linearized model. Practical methods for the design of PID controllers are proposed to stabilise the machine using voltage source inverters. Results are presented from experimental implementations which show a significant improvement in petformance over previously published results. The non-linear control technique, feedback linearization, is applied to the BDFM and shown to have some robustness to modelling enors, in a realistic simulation. An initial attempt at implementation of the scheme is reported. Preliminary results are encouraging, and warrant further investigation. Keywords: ac machines, BDFM, Brushless Doubly Fed Machines, control, coupled circuits, dq axis, equivalent circuits, feedback linearization, model reduction, parameter estimation, synchronous reference frame