  We analyze the vacuum structure of spontaneously broken N=2 supersymmetric
gauge theory with the Fayet-Iliopoulos term. Our theory is based on the gauge
group SU(2) \times U(1) with N_f=2 massless quark hypermultiplets having the
same U(1) charges. In the classical potential, there are degenerate vacua even
in the absence of supersymmetry. It is shown that this vacuum degeneracy is
smoothed out, once quantum corrections are taken into account. While there is
the runaway direction in the effective potential, we found the promising
possibility that there appears the local minimum with broken supersymmetry at
the degenerate dyon point.
