The interaction of an antiferromagnetic spin wave with a 180\ifmmode^\circ\else\textdegree\fi{} Bloch wall is studied from the theoretical point of view. Our formulation includes the anisotropy and exchange energies of the crystal together with the characteristics of the wall such as its stiffness and viscosity. The anisotropy is assumed to be of a general orthorhombic form. We show that there exists a bound wall excitation branch as well as a free spin-wave excitation branch, and we derive a restrictive set of relationships between the excitations on two different sublattices. Further, we show that there exist special values of the energy for which the spin waves are degenerate and the restrictions no longer apply. Finally, we determine the change of phase of the spin waves on passing through the Bloch wall as a function of the wavelength, demonstrate that the phase change decreases as the wavelength increases, and compare our results with those of the analogous ferromagnetic case.