Abstract This paper presents a summary of the basic principles of the supersonic compressor and an analytical study of the types of this compressor most likely to prove successful. This study assumes rather idealized conditions, ignoring such variables as radial effects and flow irregularities. Hence the results are not intended as design criteria. They should, however, give a fair guide to what may be expected of the various cases considered; their outstanding limitations, their range of operation, and their performance expectations. Conclusions are that good pressure ratios with high efficiencies may be attained; that the compressor having a normal shock in the stator is superior to that having a normal shock in the rotor; and that the largest restriction on this normal-shock-in-stator compressor is the Mach number limitation in the rotor.