We investigate the propagation of linear MHD waves, and the occurrence of the Kelvin-Helmholtz instability, along a magnetic slab in an asymmetric environment. We define the equilibrium as a steady magnetic slab embedded in a plasma with different values of pressure, density, magnetic field, and background flow on either side. We derive the dispersion relation for this system and analyse the effect of asymmetry of the equilibrium on the wave propagation along the slab. The threshold for the occurrence of the Kelvin-Helmholtz instability is obtained numerically, along with phase diagrams for the system. Applications to solar and magnetospheric physics are outlined.