A STUDY has been performed to derive a threshold criterion for the existence of turbulence in a shear layer, and to see if such a threshold is useful in predicting transition onset in such a flow. This approach has already given satisfactory results in wake flows. l As in the latter case, the present work 2 is based on the existence of a minimum turbulence Reynolds number, and derives numerical results by utilizing established magnitudes of turbulence properties in the turbulent shear layer. Transition Reynolds numbers are predicted as a function of speed ratio, total temperature ratio, and Mach number jumps across the layer. New experiments are described in which free shear-layer transition was measured and, within an observed unit Reynolds-number effect, was found to parallel the predictions quite well.