In spite of the fact that extending oils have been used very widely for many years, no fundamental work has been done to elucidate how they affect the viscoelastic behavior of elastomers. We have performed viscoelastic measurements of the oil‐polymer system over the range of polymer concentration from 2.5 to 100% and temperature range from 30 to 150°C. Polymers were ethylene‐propylene copolymer rubbers, which had been chosen to represent very different chain structures. Sample A had a relatively narrow distribution of molecular weight (MWD) and the least branching, whereas sample B had a broader MWD with some long branching and gels. The temperature‐superposition principle was determined to be applicable for these data, allowing the construction of master curves of elastic and loss moduli over eight decades of frequency. The data encompass the rubbery plateau and flow regions. We have discovered that the concentration superposition applies to only a limited range of data, when the polymer contains long branching. Nevertheless, the two superposition principles provide a basic framework for describing the material behavior, especially when the significance is attached to the manner of deviation from the concentration superposition.