We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(Nc) and Nc+N quark flavors. Nc flavors are massless, the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with Nc +N flavors of dual quark fields plus a gauge-singlet mesonic field M. The original theory is referred to as quark theory while the dual one is termed monopole theory. The suggested mild deformation of Seiberg's procedure changes the dynamical regime of the monopole theory from infrared free to asymptotically free at large distances. We show that, upon condensation of the dual quarks, the dual theory supports non-Abelian flux tubes (strings). Seiberg's duality is extended beyond purely massless states to include light states on both sides. Being interpreted in terms of the quark theory, the monopole-theory flux tubes are supposed to carry chromoelectric fields. The string junctions - confined monopole-theory monopoles - can be viewed as constituent quarks of the original quark theory. We interpret closed strings as glueballs of the original quark theory. Moreover, there are string configurations formed by two junctions connected by a pair of different non-Abelian strings. These can be considered as constituent quark mesons of the quark theory.