  We show that D/2--form gauge fields in D even dimensions can get a mass with
both electric and magnetic contributions when coupled to conformal
field--strengths whose gauge potentials is are \frac {D-2}{2}- forms. Denoting
by e^I_\L and m^{I\L} the electric and magnetic couplings, gauge invariance
requires: e^I_\L m^{J\L}\mp e^J_\L m^{I\L}=0, where I,\L= 1... m denote the
species of gauge potentials of degree D/2 and gauge fields of degree D/2-1,
respectively. The minus and plus signs refer to the two different cases D=4n
and D=4n+2 respectively and the given constraints are respectively {\rm
{Sp}}(2m) and {\rm {O}}(m,m) invariant. For the simplest examples, (I,\L=1 for
D=4n and I,\L=1,2 for D=4n+2) both the e,m quantum numbers contribute to the
mass \m=\sqrt {e^2 +m^2} . This phenomenon generalizes to $D$ even dimensions
the coupling of massive antisymmetric tensors which appear in D=4 supergravity
Lagrangians which derive from flux compactifications in higher dimensions. For
D=4 we give the supersymmetric generalization of such couplings using N=1
superspace.
