  The gauge symmetries of pure Chern-Simons theories with p-form gauge fields
are analyzed. It is shown that the number of independent gauge symmetries
depends crucially on the parity of p. The case where p is odd appears to be a
direct generalization of the p=1 case and presents the remarkable feature that
the timelike diffeomorphisms can be expressed in terms of the spatial
diffeomorphisms and the internal gauge symmetries. By constrast, the timelike
diffeomorphisms may be an independent gauge symmetry when p is even. This
happens when the number of fields and the spacetime dimension fulfills an
algebraic condition which is explicitely written.
