Shear stress development after the onset of steady shear flow was measured at 20-degrees-C for a polyisobutylene with viscosity-average molecular weight 9.6 X 10(5) at shear rates from 3.5 X 10(-4) to 3.5 X 10(-3) s-1. The initial parts of the stress growth coefficient curves at different shear rates composed a single curve. Simultaneous measurements of the differential dynamic moduli, G'(omega,gamma;t) and G"(omega,gamma;t), were made during the stress development process by intermittently superposed small sinusoidal oscillations at 0.1 Hz, which falls in the middle of the plateau zone. At a relatively low shear rate, both G' and G" showed constant values just the same as in linear viscoelasticity until a certain time elapsed. This time region corresponded to that in the above single curve. Then G' began to decrease and G" to increase. Corresponding to these changes in G' and G", the stress growth coefficient began to deviate from the single curve. The critical shear strain was near 0.15 and approximately independent of shear rate. It was concluded that the original entanglement structure of the linear polymer remains unchanged until a certain critical strain is accumulated and the nonlinear behavior in stress development corresponds to a change in the entanglement structure.