  We study the Brieskorn modules associated to a germ of holomorphic function
with non-isolated singularities, and show that the Brieskorn module has
naturally a structure of a module over the ring of microdifferential operators
of nonpositive degree, and that the kernel of the morphism to the Gauss-Manin
system coincides with the torsion part for the action of $t$ and also with that
for the action of the inverse of the Gauss-Manin connection. This torsion part
is not finitely generated in general, and we give a sufficient condition for
the finiteness. We also prove a Thom-Sebastiani type theorem for the sheaf of
Brieskorn modules in the case one of two functions has an isolated singularity.
