  The crossover transition from weak coupling at large \xi to strong coupling
at small \xi is studied in N=2 supersymmetric gauge theory with the U(N) gauge
group and N_f>N (here \xi is the Fayet--Iliopoulos parameter). We find that at
strong coupling a dual non-Abelian weakly coupled N=2 theory exists which
describes low-energy physics at small \xi. The dual gauge group is U(N_f-N).
The dual theory has N_f flavors of light dyons, to be compared with N_f quarks
in the original U(N) theory. Both theories support non-Abelian strings. In each
of these two regimes there are two varieties of physical excitations:
elementary fields and nonperturbative composite states bound by confining
strings. These varieties interchange upon transition from one regime to the
other. We conjecture that the composite stringy states can be related to
Seiberg's M fields.
