We study the dynamics of normal domains in a multifilamentary composit
e superconductor with a large amount of stabilizer outside the multifi
lamentary area. We consider the case when there is a transition layer
with high thermal and electrical resistance between the superconductor
and the stabilizer. We show the existence of localized and propagatin
g normal domains in these composites. We derive an implicit expression
for the propagation velocity of a normal domain.