  Hidden symmetries are the backbone of Integrable two-dimensional theories.
They provide classical solutions of higher dimensional models as well, they
seem to survive partially quantisation and their discrete remnants in M-theory
called U-dualities, would provide a way to control infinities and
nonperturbative effects in Supergravities and String theories. Starting from
Einstein gravity we discuss the building blocks of these large groups of
internal symmetries, and embed them in superalgebras of dynamical symmetries.
The classical field equations for all bosonic matter fields of all toroidally
compactified supergravities are invariant under such ``superdualities''.
Possible extensions are briefly discussed.
