Despite the existence of flank waveguide modes which are Kelvin-Helmholtz unstable, the flanks of the terrestrial magnetosphere are observed to be remarkably stable and free of nonlinear disturbances. We suggest the explanation may be found in a more detailed stability analysis which shows that localized disturbances are convectively unstable in the Earth's rest frame. This means that as a wave packet grows and broadens, it also propagates at a sufficiently high speed so it is convected away leaving ultimately no disturbance at any fixed point in space (as t→∞). We estimate that the magnetopause surface wave has an e-folding length of the order of an Earth radius and soon becomes nonlinear, resulting in a magnetopause boundary layer [e.g., Manuel and Samson, 1993>. In contrast, the waveguide modes (which penetrate deep into the body of the magnetosphere) should grow by no more than a factor of about e as they propagate around the flanks to the tail. This also explains why theorists have had such success at modeling basic ULF waveguide processes with linear theory and why nonlinear waves in, or disruptions to, the body of the magnetospheric flanks are not observed: Wavepackets may grow by only a small amount as they propagate into the tail. Ultimately, they leave the flank undisturbed and with the appearance of stability, although they are actually convectively unstable. ¿ 2000 American Geophysical Union