  In N=2 supersymmetric QCD with the U(N) gauge group and N_f>N we study the
crossover transition from the weak coupling regime at large \xi to strong
coupling at small \xi where \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) and the dual theory has N_f flavors of light dyons, to be compared
with N_f quarks in the original U(N) theory. Both, the original and dual
theories are Higgsed and share the same global symmetry SU(N) x SU(N_f-N) x
U(1), albeit the physical meaning of the SU(N) and SU(N_f-N) factors is
different in the large- and small-\xi regimes. Both regimes support non-Abelian
semilocal strings.
  In each of these two regimes particles that are in the adjoint
representations with respect to one of the factor groups exist in two
varieties: elementary fields and composite states bound by 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. The bulk duality that we observed translates into a two-dimensional
duality on the world sheet of the non-Abelian strings. At large \xi the
internal dynamics of the semilocal non-Abelian strings is described by the
sigma model of N orientational and (N_f-N) size moduli, while at small \xi the
roles of orientational and size moduli interchange. The BPS spectra of two dual
sigma models (describing confined monopoles/dyons of the bulk theory) coincide.
It would be interesting to trace parallels between the non-Abelian duality we
found and string theory constructions.
