The spatially developing mixing layer is investigated using both linear stability theory and numerical simulations. Temporal and spatial linear stability solutions are compared, and it is found that the temporal and spatial wave numbers are equal, the temporal frequency is a function of the spatial frequency, and the temporal and spatial growth rates have a one-to-one correspondence. Numerical simulations of the Euler equations are performed for the spatially developing mixing layer using a linear stability forcing function. Spatially developing simulations of the supersonic/supersonic and supersonic/subsonic acoustic instabilities and the KelvinHelmholtz instability are compared to temporally developing simulations and found to be in agreement.