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The dynamic stiffness properties of automotive hydraulic bushings exhibit significant amplitude sensitivity which cannot be captured by linear time-invariant models. Quasi-linear and nonlinear models are therefore proposed with focus on the amplitude sensitivity in magnitude and loss angle spectra (up to 50 Hz). Since the model parameters of a production bushing are unknown, dynamic stiffness tests and laboratory experiments are utilized to extract model parameters. Nonlinear compliance and resistance elements are incorporated, including their interactions in order to improve amplitude sensitive predictions. New solution approximations for the new system equations (containing both nonlinear compliance and resistance elements) refine the multi-term harmonic balance term method. Quasi-linear models yield excellent accuracy but lack the ability to predict trends in amplitude sensitivity since they rely on available dynamic stiffness measurements. Nonlinear models containing both nonlinear resistance and compliance elements yield superior predictions to those of prior models (with a single resistance or compliance nonlinearity), while also providing more physical insight. Suggestion for further work is briefly mentioned.