  The purpose of this paper is to show that the so-called Maxwell superalgebra
in four dimensions, which naturally involves the presence of a nilpotent
fermionic generator, can be interpreted as a hidden superalgebra underlying N =
1, D=4 supergravity extended to include a 2-form gauge potential associated to
a 2-index antisymmetric tensor. In this scenario, the theory is appropriately
discussed in the context of Free Differential Algebras (an extension of the
Maurer-Cartan equations to involve higher-degree differential forms). The study
is then extended to the Free Differential Algebra describing D=11 supergravity,
showing that, also in this case, there exists a super-Maxwell algebra
underlying the theory.
  The same extra spinors dual to the nilpotent fermionic generators whose
presence is crucial for writing a supersymmetric extension of the Maxwell
algebras, both in the D=4 and in the D=11 case, turn out to be fundamental
ingredients also to reproduce the D=4 and D=11 Free Differential Algebras on
ordinary superspace, whose basis is given by the supervielbein. The analysis of
the gauge structure of the supersymmetric Free Differential Algebras is carried
on taking into account the gauge transformations from the hidden
supergroup-manifold associated with the Maxwell superalgebras.
