  We study properties of D = 4, N >1 extended supergravities (and related
compactifications of superstring theory) and their consistent truncation to the
phenomenologically interesting models of N = 1 supergravity. This involves a
detailed classification of the "degenerations" of the duality groups of type
E7, when the corresponding quartic invariant polynomial built from the
symplectic irreducible representation of G4 "degenerates" into a perfect
square. With regard to cosmological applications, we conclude that the
consistent truncation to N = 1 from higher-dimensional or higher-N theory gives
a zero measure minimal coupling of vectors. A non-minimal coupling involving
vectors coupled to scalars and axions is generic. These features of
supergravity, following from the electric-magnetic duality, may be useful in
other applications, like stabilization of moduli, and in studies of
non-perturbative black-hole solutions of supergravity/string theory.
