The most commonly used definition for human tremor is as an involuntary, roughly sinusoidal oscillation of one or more parts of the body. It has been established that the application of viscous damping can significantly reduce the amplitude of tremor related oscillations, but that the level of damping required also impedes voluntary motion. Evidence would suggest that if a controllable damper were used, then it may be possible to modulate the damping so as to provide a significant level of tremor suppression, while allowing voluntary motion. A candidate for the construction of such a damper is electrorheological (ER) fluid. When an electric field is applied to a volume of ER fluid, its material properties change from that of a Newtonian fluid to that of an elastic-plastic solid. These structural changes occur within milliseconds and are completely reversible, making ER fluids an attractive option when designing controllable dampers. The analysis and design of control strategies for ER dampers requires the development of suitable mathematical models. In particular, models should be capable of predicting the dominant behaviour of the device when coupled to other physical systems. In this thesis, well known thermomechanical principles are used to develop simple, physically intuitive models which are well suited for analysis and control design. The simplest of these damper models is then coupled with a forced, second order oscillator, representing the human forearm/elbow subject to tremor. A detailed analysis of the qualitative behaviour of this system is then performed, using traditional energy based and Liapunov type techniques. Sufficient conditions for the existence and stability of periodic solutions are also presented. A result of this analysis is the development of a novel control strategy for the attenuation of periodic oscillations. In the final section of the thesis, the feasibility of using the above mentioned control strategy for suppression of human tremor is investigated. The theoretical results are quite favourable and are supported by numerous simulation results.