We show that all branes admit worldvolume domain wall solutions. We fi
nd one class of solutions for which the tension of the brane changes d
iscontinuously along the domain wall. These solutions are not supersym
metric. We argue that there is another class of domain wall solutions
which is supersymmetric. A particular case concerns supersymmetric dom
ain wall solutions on IIB D-5- and NS-5-branes. (C) 1998 Published by
Elsevier Science B.V. All rights reserved.