  We investigate non-local dualities between suitably compactified
higher-dimensional Einstein gravity and supergravities which can be revealed if
one reinterprets the dualised Kaluza-Klein two-forms in $D>4$ as antisymmetric
forms belonging to supergravities. We find several examples of such a
correspondence including one between the six-dimensional Einstein gravity and
the four-dimensional Einstein-Maxwell-dilaton-axion theory (truncated N=4
supergravity), and others between the compactified eleven and ten-dimensional
supergravities and the eight or ten-dimensional pure gravity. The Killing
spinor equation of the D=11 supergravity is shown to be equivalent to the
geometric Killing spinor equation in the dual gravity. We give several examples
of using new dualities for solution generation and demonstrate how $p$-branes
can be interpreted as non-local duals of pure gravity solutions. New
supersymmetric solutions are presented including $M2\subset 5$-brane with two
rotation parameters.
