Simultaneous measurements of stress relaxation and differential dynamic modulus were made at 268 K over a time scale of 10-to 10(4.5) s for nearly monodisperse polybutadiene (M-w = 2.2 x 10(5), 1,2-structure 70%, M-e = 3600) and also one having coarse cross-linking (M-c = 29000). Static shear strain ranged from 0.1 to 2.0. In a long-time region (t > tau(k)), the relaxation modulus G(gamma;t) could be expressed by the product G(0;t)h(gamma). The observed h(gamma) agreed well with the Doi-Edwards theory without use of IA approximation. Both the cured and uncured samples showed initial drop of the differential storage modulus G＇(omega,gamma; t) followed by gradual recovery, but did not attain the value before shearing G＇(omega,gamma; t) for the uncured sample showed smaller values than that for the cured one in the whole measured time scale at the higher strain, confirming the two origins of nonlinear viscoelasticity of well entangled polymer; induced chain anisotropy and induced decrement in entanglement density. G＇(omega,gamma; t) curves for the cured sample agreed well with the BKZ predictions. But the curves for the uncured sample agreed well with the BKZ prediction only at the time scale of t < tau(k) BKZ prediction showed significant upward deviations at t > tau(k) Such the differences are discussed in terms of the two origins.