  We introduce a doubled formalism for the bosonic sector of the maximal
supergravities, in which a Hodge dual potential is introduced for each bosonic
field (except for the metric). The equations of motion can then be formulated
as a twisted self-duality condition on the total field strength \G, which takes
its values in a Lie superalgebra. This doubling is invariant under
dualisations; it allows a unification of the gauge symmetries of all degrees,
including the usual U-dualities that have degree zero. These ``superdualities''
encompass the dualities for all choices of polarisation (i.e. the choices
between fields and their duals). All gauge symmetries appear as subgroups of
finite-dimensional supergroups, with Grassmann coefficients in the differential
algebra of the spacetime manifold.
