This report presents the results of a study of hypervelocity flows, with particular emphasis on the similitude requirements. A primary objective has been to delineate the similitude parameters for certain typical flows and, where possible, to evaluate the effects of not duplicating all of the similitude parameters in wind-tunnel tests. As a part of this study, a comprehensive review of inviscid and viscous similitude is given, as well as a state-of-the-art survey of flow solutions. It is shown that in many instances there do not exist, at present, sufficient experimental data or theoretical solutions to evaluate the sensitivity of various flow quantities to variations in the similitude parameters nor to determine whether some similitude parameters are less important than others. Such an evaluation has been accomplished for certain simple flows, such as wedges, cones, blunt-nosed flat plates and stagnation- region flows. For these flows it is found that in the flight regime of interest (velocities from 10,000 to 36,000 fps and altitudes from 50,000 ft. to 250,000 ft.) duplication of density-altitude and free-stream velocity are more important than duplication of free-stream Mach number (i.e., temperature). However, lack of duplication of Mach number can introduce significant errors in the case of slender bodies. Other topics that have been investigated are the effects of alkali-metal seed on hypervelocity flows, the importance of simulating ablation phenomena in wind-tunnel tests, and the testing time requirements for hypervelocity wind tunnels. (Author).