A linear analysis of the Kelvin-Helmholtz instability is performed by assuming that one of the plasma regimes (magnetosphere) separated by a velocity shear layer of zero thickness is spatially nonuniform. The previous theories based on the semi-infinite uniform model with infinitesimally thin magnetopause showed that wave growth due to the Kelvin-Helmholtz instability exhibits monotonic increase for shorter frequency. This finding implies that no monochromatic waves whose spatial scales are as large as the magnetospheric size are generated by the Kelvin-Helmholtz instability. In contrast, the present analysis reveals that the Kelvin-Helmholtz instability generates global-scale monochromatic waves when the magnetosphere is nonuniform and the magnetosheath flow speed is quite fast. The wave number is given through the dispersion relation of the Kelvin-Helmholtz unstable wave. ¿ American Geophysical Union 1996