Domain Walls on the Brane

We show that all branes admit worldvolume domain wall solutions. We find one class of solutions for which the tension of the brane changes discontinuously along the domain wall. These solutions are not supersymmetric. We argue that there is another class of domain wall solutions which is supersymmetric. A particular case concerns supersymmetric domain wall solutions on IIB D-5- and NS-5-branes.