Two-dimensional, compressible turbulent shear layers are studied in a new wind tunnel facility. Helium, nitrogen and argon gases are used in various combinations to produce shear layers with isentropically computed convective Mach numbers that range from near zero to unity. Side-view Schlieren photographs of these compressible flows are generally devoid of the two-dimensional, large-scale structures seen in incompressible flows. Travelling shock and expansion waves are observed in the high compressibility flows, evidently created by turbulent structures convecting at supersonic velocities with respect to one of the free streams. Such waves are seen only in the low speed fluid, with apparent convection velocities much higher than those predicted by the usual isentropic pressure-matching arguments. The measured shear layer growth rates agree with previous results by other experimenters, except for a few unusual cases at low compressibility and low density ratio. Finally, it is observed that the shear layer growth rate is relatively insensitive to the effects of incident shock and expansion waves on the shear layer.