This thesis presents a study of two outstanding problems in eddy-current coupling theory: (a) the steady-state performance of copper-faced couplings. (b) the transient performance of eddy-current couplings. After a general introductory chapter which reviews the problems of coupling analysis and existing theories of the machine, the work falls, broadly, into two parts. The first part (chapters 2-4) presents a three-dimensional theory of the copper-faced coupling and describes experiments designed to test the validity of the theory. The second part (chapters 5-9) is devoted to the transient performance of eddy-current couplings; in particular, torque response at constant slip speed. After reviewing existing practice and possible theoretical approaches, a theory, based on the transient solution of the diffusion equation, is developed. Experiments on a new test machine, which investigate the assumptions of the theory and the method of torque prediction, are discussed in detail.