A new constitutive model for the nonlinear behavior of noncrosslinked polymers with infinitesimal strains is derived. It generalizes a model of adaptive links for the viscoelastic behavior of crosslinked polymers. According to the model, a viscoelastic medium is treated as a set of elastic springs that replace each other. The springs model chemical links between polymer molecules, which arise and collapse because of the micro-Brownian motion, a law for replacing the springs determines the stress relaxation in a viscoelastic medium. Unlike crosslinked polymers, noncrosslinked polymers demonstrate steady-state creep flow after some transition period. To describe both the transition process and the steady creep, the model distinguishes two different types of adaptive links, Links of the first type are ruptured under loading, whereas links of the second type replace one another. Both these processes (destruction and replacement) are treated as kinetic, and equations of chemical kinetics are introduced for their description. The nonlinearity of the model arises because of a dependence of rates of kinetic processes on the stress intensity. The constitutive equations derived are testified by comparing theoretical results with data for polypropylene fibers. For the verification we use data presented by three independent sources. The results demonstrate good agreement between experimental observations and their theoretical predictions. Finally, the effect of molecular weight of polymers on parameters of the model is studied.