The Maxwell orthogonal rheometer was used to measure the limit of linear viscoelastic response (LLVER) as a function of frequency for three linear polyethylenes at 170°C, for six atactic polystyrenes at 170°C, and for Phenoxy A at 212°C. For the elastic component of the stress, linear viscoelastic response was found to exist in all cases up to finite strains of approximately 50%. The viscous component of the stress exhibited linear viscoelastic response up to approximately 100% strain and sometimes as high as 120%, the maximum strain tested. Two constitutive equations (Bird and Carreau's theory with Gordon and Schowalter's generalization and Tanner's network rupture theory) are noted for the dependence they predict of the strain LLVER as a function of frequency. Bird's theory, with Gordon and Schowalter's generalization, predicts that the elastic strain limit times the frequency will be a constant as the frequency is varied; Tanner's theory predicts that the elastic strain limit will be a constant with varying frequency. Data are shown to support Tanner's theory. Although the theories predict similar relations for the viscous strain limit, since no viscous limit is found up to 120% strain, this portion of the theories could not be checked. Plots of the reduced in‐phase modulus, G′(γ)/GL′, and the reduced in‐phase viscosity, η′(γ)/ηL′, versus strain, γ, (GL′ and ηL′ are the modulus and viscosity below the limit) yield very similar curves for all the polymers. This is in agreement with the limited data from MacDonald, Marsh, and Ashare. The reduced in‐phase modulus is constant as the strain is increased up to the elastic LLVER. A gradual decrease then occurs for all of the polymers; at 120% strain, the reduced modulus has decreased between 20 and 30%.