  We find explicit expression for the one-loop four-graviton amplitude in
eleven-dimensional supergravity compactified on a circle. Represented in terms
of the string coupling (related to the compactification radius) it takes the
form of an infinite sum of perturbative string loop corrections. We also
compute the amplitude in the case of compactification on a 2-torus which is
given by an SL(2,Z) invariant expansion in powers of the torus area. We discuss
the structure of quantum corrections in eleven-dimensional theory and their
relation to string theory.
