  We study the connection between N=2 supersymmetry and a topological bound in
a two-Higgs-doublet system having an $SU(2)\times U(1)_Y\times U(1)_{Y'}$ gauge
group. We derive Bogomol'nyi equations from supersymmetry considerations
showing that they hold provided certain conditions on the coupling constants,
which are a consequence of the huge symmetry of the theory, are satisfied.
