In this thesis, the problem of controlling both transient and asymptotic behaviour of solutions of functional differential equations is addressed. The work begins, in Chapter 1, with an introduction to basic control theory principles that will be used throughout. This is followed by the introduction of a class of nonlinear operators in Chapter 2 and the development of suitable existence theories for the associated system classes of functional differential equations and inclusions in Chapter 3. A discussion is provided, in Chapter 2, describing diverse phenomena, such as delays and hysteresis, that can be incorporated in the class of operators. Chapters 4-7 cover four areas of research. Chapter 4 examines the asymptotic and transient behaviour of nonlinearly-perturbed linear systems of known relative degree; a continuous feedback strategy is adopted and an approximate tracking result is presented. In Chapter 5 the class of systems considered is expanded to a large class of nonlinear systems and a continuous feedback strategy is implemented in order to achieve approximate tracking. In Chapters 6 and 7 attention is restricted to systems <;>f relative degree one, but this limitation is compensated for by targeting an exact asymptotic tracking result. The first investigation, in Chapter 6, involves a potentially discontinuous feedback controller applied to a class of nonlinear systems, with comparisons made to an internal model approach. Asymptotic tracking and approximate tracking are developed in unison within a framework of functional differential inclusions. Finally, in Chapter 7, a continuous controller is applied to single-input, single-output, nonlinear systems with input hysteresis.