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The local segmental dynamics of cis‐polybutadiene in dilute solutions have been investigated using natural abundance 13C NMR spectroscopy. The time integral of the CH orientation autocorrelation function 〈σ〉 is extracted from T1 measurements in five solvents covering a viscosity range of two decades. The hydrodynamic Kramers' equation, which is generally assumed to be appropriate for local polymer dynamics in dilute solution, cannot describe these results. 〈σ〉 is found to depend upon the solvent viscosity η raised to the 0.33 power whether η is varied by changing the temperature or the solvent. This apparent power law behavior has been observed for other polymers in dilute solution and can be rationalized if the solvent is viewed as viscoelastic. This view is supported by experimental results which show that local polymer dynamics can occur as much as an order of magnitude faster than solvent reorientation. Trends for a mixed microstructure polybutadiene are similar to those of cis‐polybutadiene. © 1994 John Wiley & Sons, Inc.