The gauge symmetries of pure Chem-Simons theories with p-form gauge fi
elds are analysed. It is shown that the number of independent gauge sy
mmetries 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 expres
sed in terms of the spatial diffeomorphisms and the internal gauge sym
metries. In contrast, the timelike diffeomorphisms may bt:independent
gauge symmetries when p is even. This happens when the number of field
s and the spacetime dimension fulfil an algebraic condition which is w
ritten explicitly.