  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=1,2 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. In N_f=1 case,
the effective potential is found to be so-called runaway type, and there is
neither well-defined vacuum nor local minimum. On the other hand, in N_f=2
case, while there is also the runaway direction in the effective potential, we
find the possibility that there appears the local minimum with broken
supersymmetry at the degenerate dyon point.
