The non-equilibrium supersonic flow of a relaxing or reacting gas through a plane expansion has been studied from a numerical,, analytical and experimental point of view. The flow of an ideal dissociating gas in a two dimensional expansion has been solved numerically by writing the governing equations of motion in their characteristic form. In conflict with linearised theory along the wall, the numerical solutions do not asymptote to the infinite rate equilibrium values. To estimate how far the asymptotic state deviates from the infinite rate equilibrium values, a formal second order solution has been developed with the aid of transform techniques. An example has been discussed for a simplified relaxing gas model, and estimates of the asymptotic state have been obtained. An exact solution over the whole field was not possible but by treating the parameter as small, an approximate answer has been found. To understand in more detail the coupling effects of two relaxation processes, linearised theory has been extended to cope with the flow of a gas with more than one relaxing mode. An example has been discussed far Carbon Dioxide and the effect of possible coupling between the bending and stretching modes of the molecule in a plane expansion has been investigated. The Mach-Zehnder interferometer and Schlieren method have been used in conjunction with a 2" - diameter shock tube to study the density and density gradients within, and following a sharp two-dimensional expansion for shock heated Carbon Dioxide. Measurement of the density gradient at the leading edge of the expansion by quantitative Schlieren methods have allowed relaxation times to be obtained. This method has the advantage that relaxation times can be obtained for specific values of the density and temperature for only small departures from an equilibrium state.