  Composite non-Abelian vortices in N=2 supersymmetric U(2) SQCD are
investigated. The internal moduli space of an elementary non-Abelian vortex is
CP^1. In this paper we find a composite state of two coincident non-Abelian
vortices explicitly solving the first order BPS equations. Topology of the
internal moduli space T is determined in terms of a discrete quotient CP^2/Z_2.
The spectrum of physical strings and confined monopoles is discussed.
  This gives indirect information about the sigma model with target space T.
