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It is shown by theoretical analysis that domain walls can support two different types of waves denoted as "magnetostatic interface waves" and "wall displacement waves". The magnetostatic interface waves are similar in character to magnetostatic surface waves. The wall displacement waves are analogous to displacement waves on strings and to capillary waves on the surface of liquids, Dispersion relations are derived for both types of waves. The displacement waves are approximately dispersion free at high wavenumbers. At low wavenumbers their dispersion diagram reflects the incipient instability of the straight domain wall against sinusoidal displacement, which occurs as the field gradient is reduced.