High molecular weight linear polymers and their concentrated solutions were investigated over a wide range of frequencies and amplitudes of oscillatory deformation. At definite critical deformation and stress amplitudes, the resistance to deformation drops abruptly as a result of the rupture of continuity of polymer specimens in the region of action of the highest shear stresses. The lowest critical values of deformation rate amplitudes are inversely proportional to the initial viscosity and correspond quantitatively to the critical shear rates at which the spurt occurs during the flow of polymeric systems in ducts. The spurt effect is due to the transition of the polymer systems to the forced high-elastic state, in which they behave like quasi-cured polymers whose deformability is always limited. Up to the critical values of the stress amplitudes, narrow-distribution high molecular weight linear flexible-chain polymers behave like Hookean bodies, whereas the broad-distribution polymers show a sharply defined nonlinear behavior which asymptotically passes to a spurt. The amplitude dependence of the dynamic characteristics of the high molecular weight linear polymers, as well as their non-Newtonian behavior, is due to polymolecularity. An increase in deformation amplitudes reduces the frequency at which the spurt, and hence the transition of the polymer systems to the high-elastic state, is observed. Therefore, under conditions of oscillatory deformation the physical state (fluid or high-elastic) is determined not only by the frequency but also by the value of deformation. In the high-elastic state region (estimated at low amplitude deformation), the critical deformation amplitude is frequency independent and has an unambiguous relationship with the molecular mass of the chain (Me) between the entanglements. For the bulk polymers studied, the spurt in the high-elastic state occurs at stress amplitudes of the order of 105 N/m2 irrespective of frequency, molecular mass, or polymolecularity. In concentrated polymer solutions, in the high-elastic state the critical stress amplitudes decrease with reducing polymer content, whereas the critical deformation amplitudes increase.