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We found an anomalous nonlinear behavior under large amplitude oscillatory shears, where the amplitude stress deviates strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. This phenomenon is usually accompanied with the Payne effect of filled rubbers. In order to understand the molecular details regarding this unusual behavior, we examined a series of polybutadiene/tetradecane solutions filled with carbon black. Our results show that there is a previously unrecognized transition in the system as the matrix polymer concentration ϕ approaches and passes through a characteristic polymer concentration ϕc. Below ϕc, the system typically shows the classic nonlinearity, where the storage modulus G′ decreases as the strain amplitude γ0 increases and the resulting stress waveforms are distorted from sinusoidal waves. Above ϕc, the system displays an anomalous nonlinearity, where the stress responses at any given strain remain surprisingly sinusoidal regardless of the drop in the storage modulus G′. The critical concentration ϕc is about an order of magnitude greater than the entanglement polymer concentration ϕe. The degree of entanglement in the matrix apparently determines the occurrence of this unusual rheological event and plays a key role here. Increasing the polymer molecular weight enhances this transition. [ABSTRACT FROM AUTHOR]