  We show that in heterotic string theory compactified on a six dimensional
torus, the lower bound (Bogomol'nyi bound) on the dyon mass is invariant under
the SL(2,Z) transformation that interchanges strong and weak coupling limits of
the theory. Elementary string excitations are also shown to satisfy this lower
bound. Finally, we identify specific monopole solutions that are related via
the strong-weak coupling duality transformation to some of the elementary
particles saturating the Bogomol'nyi bound, and these monopoles are shown to
have the same mass and degeneracy of states as the corresponding elementary
particles.
