The present work reports theoretical and experimental investigations on supersonic axisymmetric parallel diffusers and ejectors with a view to obtaining their design and performance criteria. In large-scale engine test facilities the exhaust gases are discharged into the test cell at low ambient pressure corresponding to that at high altitudes. This is-also the pressure at entry to the diffuser which accepts the gases and simultaneously recompresses them to the ambient diffuser-exit pressure by a system of shock waves. The nozzle back pressure drops rapidly with in-creasing blowing pressure at the nozzle inlet when a single normal shock standing close to the nozzle exit plane compresses the gases. At a sufficiently high blowing pressure the normal shock breaks down into an oblique shock system when the nozzle back pressure reaches a minimum. It now increases with the blowing pressure, and the diffuser-operating condition is said to be "started" having previously been "unstarted". Because of the above differences, the flow at the diffuser entry for the unstarted and started operating conditions are separately analysed. Consideration of the unstarted diffuser rests on a force-momentum balance across a specified control volume, assuming a turbulent boundary laypr to grow from.the nozzle throat and at the nozzle outlet to be describable in terms of dis-placement and momentum thicknesses. The Korst - Chapman model for the analogous step-down cylinder base flow problem is used to analyse the inlet region of the started diffuser. This leads to the equations defining the shear-layer momentum thickness and relating it to that of the separating boundary layer. Transformation of the axisymmetric equations to their two-dimensional equivalents and incorporation of a suitable velocity distribution for the mixing layer together with an empirical reattachment parameter yield an expression from which diffuser entry pressure can be evaluated by either a graphical or an iterative procedure for given initial conditions. Good agreement is obtained between predictions and measurements for both the unstarted and the started diffuser, especially for larger diffuser area ratios. The shock - boundary layer interactions in the re-attachment region and downstream lead to high heat transfer rates in the diffuser. An approximate analysis of the flow downstream of reattachment in a started diffuser leads to satisfactory agreement between the predicted Stanton number and experimental results. For the separated and reattachment regions, however, empirical relations between local Stanton number and Reynolds number are obtained from heat transfer measurements. The sudden enlargement in flow area (where the supersonic stream from the exhaust nozzle enters the diffuser) allows for the injection of a secondary fluid when the device serves as an ejector. Measurements are reported of the effect on the nozzle back pressure, the adiabatic wall temperatures and wall heat transfer of secondary injection into a parallel diffuser through the sudden enlargement at the junction with the nozzle generating the supersonic primary flow. The range of mass ratio covers both subsonic and supersonic flow through the variable-area secondary port. The stagnation temperature of the primary flow is varied, while that of the secondary flow is kept constant. With increasing mass ratio, the nozzle back pressure passes first through a maximum and then a minimum to reach a plateau value greater than that for zero secondary flow. Correlations for film-cooling effectiveness with downstream distance from the point of secondary injection show mainly qualitative agreement with sub-sonic film-cooling predictions and for low mass-velocity ratios suggest greater effectively-cooled lengths in supersonic flow. The optimisation of diffuser-ejector design is considered in the light of the investigation. Copies of two papers written wholly on the basis of the present work are submitted along with the thesis. They are inserted in a pocket in the rear cover of Volume II.