A ferromagnetic crystal with cubic and induced orthorhombic and uniaxial anisotropies is considered. The hard uniaxial anisotropy axis is parallel to the [110] direction, the hard orthorhombic axis parallel to the [1¯10] direction. Localized spin waves propagating along a single domain wall in such materials are analyzed by numerical solution of the Landau–Lifshitz and magnetostatic equations. The spin wave spectra are calculated for propagation directions either perpendicular or parallel to the direction of the magnetization in the two adjacent domains. There exist critical combinations of magnetic anisotropy constants for which the uniform Bloch wall becomes unstable before the Neel wall is preferred. In such parameter regions Goldstone modes show a gap in the wave number and a loop of the dispersion branch for the case of perpendicular propagation. This behavior is very similar to that of hydrodynamic waves excited in stratified shear flows. The existence of negative energy waves and the appearance of a Kelvin–Helmholtz instability are to be expected for spin waves propagating along an initially plane domain wall in the absence of dissipation. All spectra for perpendicular propagation are asymmetric with respect to wave vector inversion. They also contain the unidirectional Gilinskii-type mode which has a finite frequency at zero wave number. This activation frequency coincides with the frequency of the bottom of the bulk spin wave manifold for propagation parallel to domain magnetizations. Measurements of resonant excitations of single domain walls in bismuth-substituted garnet films with in-plane magnetization are presented. The resonances are observed in the frequency range from 50 to 1500 MHz. They are qualitatively discussed on the basis of the developed theory. ©1997 American Institute of Physics.