The equation for the pressure fluctuations in a turbulent boundary layer are derived with special reference to their values at a rigid wall. It is shown that in incompressible flow the pressure field is defined completely once the velocity field is known. The results obtained from the theory are compared with experiment. The work is extended to include the effects of compressibility and it is found that a treatment similar to that given by Phillips is appropriate. It is shown that under conditions of zero heat transfer the theory slightly modified by the effects Mach numbers eddy Mach waves ace pressure distribution throughout obtained in incompressible flow is only of compressibility. However, at higher formed and these modify to some extent the the layer, and in particular at the wall. In addition strong radiation of sound occurs under conditions of flow external to the boundary layer. supersonic Comparisons with experiment show moderate agreement. The theories as mentioned previously are for the case of zero external pressure gradient, but it is shown that even when these conditions are relaxed similar results occur. Some experimental results in support of this conclusion are presented.