In this paper observations by the vector electron spectrometer on the ISEE 1 spacecraft are used to directly check the incompressible hydrodynamic stability condition given by Hasegawa (1975), which indicates how stability is influenced by the velocity shear, density ratio, magnetic field, and the direction of the wave vector of the unstable wave mode. Since the plasma quantities can be measured, the stability can be examined by means of a contour plot of the stability condition in &thgr;, ϕ space, where &thgr; is the polar angle and ϕ the azimuthal angle specifying the wave direction assumed. The magnetopause is generally found to be stable, by a large margin. In contrast, many cases of marginal stability or instability are found across density transitions in, and at the inner edge of, the boundary layer for wave vectors in plausible directions. It thus appears that the Kelvin-Helmholtz instability is of importance at the inner edge of the magnetospheric boundary layer, as predicted by magnetohydrodynamic theory. ¿ American Geophysical Union 1989