Accurate monitoring of creep- and fatigue-based degradation in engineering components has become increasingly important within the power generation industry in recent years. One feature associated with the presence of such degradation, particularly in its early stages, is a certain amount of 'nonlinearity' in the ultrasonic response of a component. This nonlinear response is known to be sensitive to microstructural changes in the propagation medium, even before the stage where larger-scale features of damage may produce a measurable linear response. Measuring changes in signal nonlinearity therefore represents a promising means of material characterisation during the onset stages of component deterioration. The work in this thesis is based on the second hannonic generation method - an ultrasonic inspection technique which exploits the generation of higher harmonics in a nonlinearly propagating sinusoidal signal. Many recent experimental studies have found second harmonic measurements to be a strong indicator of increasing levels of creep and fatigue damage in laboratory specimens. However, while the theoretical aspects of harmonic generation in solids are generally quite well understood, the practical implementation of the technique is still at a relatively early stage in its development. Because of this, damage assessment experiments have generally only been qualitative in their estimations of nonlinearity. A large part of the work here is aimed at exploring improvements to the ways in which harmonic generation measurements are made and interpreted. Firstly, by developing a model representative of a typical measurement, the effects of various experimental parameters on the accuracy of the outcome are assessed. Here, theoretical and experimental results show that significant improvements in measurement interpretation can be made by including factors which are generally overlooked. The model is then used to explore alternative practical methods of implementation of the technique. Here a single-sided measurement configuration is explored, the feasibility of which is confirmed experimentally. Finally, a method is proposed to provide an increased level of detail regarding the distribution of nonlinearity within a component.