  We analyse the global (rigid) symmetries that are realised on the bosonic
fields of the various supergravity actions obtained from eleven-dimensional
supergravity by toroidal compactification followed by the dualisation of some
subset of fields. In particular, we show how the global symmetries of the
action can be affected by the choice of this subset. This phenomenon occurs
even with the global symmetries of the equations of motion. A striking
regularity is exhibited by the series of theories obtained respectively without
any dualisation, with the dualisation of only the Ramond-Ramond fields of the
type IIA theory, with full dualisation to lowest degree forms, and finally for
certain inverse dualisations (increasing the degrees of some forms) to give the
type IIB series. These theories may be called the GL_A, D, E and GL_B series
respectively. It turns out that the scalar Lagrangians of the E series are
sigma models on the symmetric spaces K(E_{11-D})\backslash E_{11-D} (where K(G)
is the maximal compact subgroup of G) and the other three series lead to models
on homogeneous spaces K(G) \backslash G\semi \R^s. These can be understood from
the E series in terms of the deletion of positive roots associated with the
dualised scalars, which implies a group contraction. We also propose a
constrained Lagrangian version of the even dimensional theories exhibiting the
full duality symmetry and begin a systematic analysis of abelian duality
subalgebras.
