  In $d$ dimensions, the model for a massless $p$-form in curved space is known
to be a reducible gauge theory for $p>1$, and therefore its covariant
quantisation cannot be carried out using the standard Faddeev-Popov scheme.
However, adding a mass term and also introducing a Stueckelberg reformulation
of the resulting $p$-form model, one ends up with an irreducible gauge theory
which can be quantised \`a la Faddeev and Popov. We derive a compact expression
for the massive $p$-form effective action, $\Gamma^{(m)}_p$, in terms of the
functional determinants of Hodge-de Rham operators. We then show that the
effective actions $\Gamma^{(m)}_p$ and $\Gamma^{(m)}_{d-p-1}$ differ by a
topological invariant. This is a generalisation of the known result in the
massless case that the effective actions $\Gamma_p$ and $\Gamma_{d-p-2}$
coincide modulo a topological term. Finally, our analysis is extended to the
case of massive super $p$-forms coupled to background ${\cal N}=1$ supergravity
in four dimensions. Specifically, we study the quantum dynamics of the
following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet;
and (iii) three-form multiplet. It is demonstrated that the effective actions
of the massive vector and tensor multiplets coincide. The effective action of
the massive three-form is shown to be a sum of those corresponding to two
massive scalar multiplets, modulo a topological term.
