  The effective action for type II string theory compactified on a six torus is
$N=8$ supergravity, which is known to have an $E_{7}$ duality symmetry. We show
that this is broken by quantum effects to a discrete subgroup, $E_7(\Z)$, which
contains both the T-duality group $SO(6,6;\Z)$ and the S-duality group
$SL(2;\Z)$. We present evidence for the conjecture that $E_7(\Z)$ is an exact
\lq U-duality' symmetry of type II string theory. This conjecture requires
certain extreme black hole states to be identified with massive modes of the
fundamental string. The gauge bosons from the Ramond-Ramond sector couple not
to string excitations but to solitons. We discuss similar issues in the context
of toroidal string compactifications to other dimensions, compactifications of
the type II string on $K_3\times T^2$ and compactifications of
eleven-dimensional supermembrane theory.
