  The electric-magnetic duality transformation in four dimensional heterotic
string theory discussed by Shapere, Trivedi and Wilczek is shown to be an exact
symmetry of the equations of motion of low energy effective field theory even
after including the scalar and the vector fields, arising due to
compactification, in the effective field theory. Using this duality
transformation we construct rotating black hole solutions in the effective
field theory carrying both, electric and magnetic charges. The spectrum of
extremal magnetically charged black holes turns out to be similar to that of
electrically charged elementary string excitations. We also discuss the
possibility that the duality symmetry is an exact symmetry of the full string
theory under which electrically charged elementary string excitations get
exchanged with magnetically charged soliton like solutions. This proposal might
be made concrete following the suggestion of Dabholkar et. al. that fundamental
strings may be regarded as soliton like classical solutions in the effective
field theory.
