  We consider the theory of closed $p$-branes propagating on
$(p+1)$-dimensional space-time manifolds. This theory has no local degrees of
freedom. Here we study its canonical and BRST structures of the theory. In the
case of locally flat backgrounds one can show that the $p$-brane theory is
related to another known topological field theory. In the general situation
some equivalent actions can also be written for the topological $p$-brane
theory.
