The instability of the magnetopause caused by the resonant interaction of a negative energy surface wave with Alfv¿n waves localized in the vicinity of the resonant magnetic surface is considered. The most important property of this instability is that it takes place for flow velocities in the magnetosheath below the Kelvin-Helmholtz (KH) threshold velocity, i.e., when there is no KH instability of the magnetopause. The magnetopause is modeled by an MHD tangential discontinuity with a magnetic-free plasma on the magnetosheath side and cold plasma on the magnetospheric side. It is shown that one of the two surface waves that propagate along the discontinuity when the shear velocity is smaller than the KH threshold velocity is a negative energy wave when the shear velocity is larger than a critical velocity. This negative energy wave propagates tailward in the magnetospheric frame, although it propagates sunward in the magnetosheath frame. When, in addition, a resonant condition is satisfied, the negative energy surface wave resonantly interacts with localized Alfv¿n waves. This interaction results in growth of both the surface wave and the Alfv¿n waves. The resonant condition can only be satisfied when the plasma density increases and, consequently, the Alfv¿n velocity decreases in the direction toward the magnetopause in its vicinity. The increment of the resonant instability is calculated under the assumption that the plasma density changes only in a slab in the vicinity of the magnetopause with the thickness much smaller than the wavelength. The possible observational signatures of the resonant instability are discussed. ¿ 1998 American Geophysical Union