Surface waves on the inner boundary of the low-latitude boundary layer (LLBL) are considered as a possible cause for dayside high-latitude travelling convection vortices (TCVs). A dispersion equation for the surface waves with regard to their attenuation in the ionosphere is deduced. The current system of the surface wave is consistent with a pair of upward and downward field-aligned currents. The wave velocity depends upon the wavelength; taking the latter to be equal to 1000 km in the ionosphere, which is typical for the TCVs, we obtain the velocity of these waves to be to about 50--100 km/s in the magnetosphere, which corresponds to several kilometers per second in the ionosphere. The surface waves on the LLBL inner boundary may be generated by a sharp deflection of this boundary from the equilibrium position. A cause of this may be sudden impulses of the solar wind dynamic pressure or bursty reconnection at the dayside magnetopause. Surface waves may play an important role in the relaxation of the magnetosphere. The velocity of the surface waves on the LLBL inner edge is close to or slightly less than the magnetosheath plasma velocity near the magnetopause; the movement of the magnetosheath plasma along the magnetopause with a speed more than that of the surface waves may favor the formation of impulsive TCVs. It follows from the considered mechanism that the disturbance maximum is to be observed on the LLBL inner edge, and the TCV velocity has to increase with the wavelength that might be verified from experimental data.¿ 1997 American Geophysical Union