Polybutadienes (PBs) of narrow molecular weight distributions with high 1,4-microstructure were synthesized by sec-butyllithium-initiated, living polymerization. The shoulder-like anomalous behavior of the storage modulus G＇(omega) in the terminal zone for PBs was studied using size exclusion chromatography (SEC) and rheometric mechanical spectrometry (RMS). It was found that a high-molecular-weight fraction in the PBs was the main reason for the occurrence of the shoulders. The linear viscoelastic spectra were successfully obtained by the Pade-Laplace method from experimental dynamic data, using either the dynamic storage, G＇(omega), or loss, G "(omega), modulus. Both the dynamic moduli and stress relaxation in the linear regime were then calculated with reasonable precision. The feasibility of time-temperature-molecular weight superposition for PBs using this method was demonstrated. The dependencies of relaxation spectra on temperature and molecular weight were obtained by a fitting procedure. Thus, with a known reference state, the relaxation spectrum for a given molecular weight PB at a given temperature can be predicted. The predicted dynamic moduli are in good agreement with experimental data.