  We discuss the form of the string-loop-corrected effective action obtained by
compactification of the heterotic string theory on the manifold $K3\times T^2$
or on its orbifold limit and the loop-corrected magnetic black hole solutions
of the equations of motion. Effective 4D theory has N=2 local supersymmetry.
Using the string-loop-corrected prepotential of the N=2 supersymmetric theory,
which receives corrections only from the string world sheets of torus topology,
we calculate the loop corrections to the tree-level gauge couplings and solve
the loop-corrected equations of motion. At the string-tree level, the effective
gauge couplings decrease at small distances from the origin, and in this region
string-loop corrections to the gauge couplings become important. A possibility
of smearing the singularity of the tree-level supersymmetric solution with
partially broken supersymmetry by quantum corrections is discussed.
