Phase separation processes following high-rate extension in unentangled polymer solutions are studied theoretically. The flow-induced demixing is associated with the coil-stretch transition predicted in high-molecular-weight polymer solutions at high-enough Weissenberg numbers. The developed mean-field theory is valid in the dilute/semidilute solution regime, where the stretched coils overlap strongly. We elucidate and discuss the main kinetic stages of the polymer/solvent separation process including (i) growth of concentration fluctuations and formation of oriented protofibrils by anisotropic spinodal decomposition; (ii) development of welldefined highly oriented and stiff fibrils forming an anisotropic network (cross-linked fiber); (iii) microphase separation and lateral collapse of the network yielding dense oriented fiber. These novel predictions are in qualitative agreement with the experimental data. (C) 2017 Wiley Periodicals, Inc.