Aiming at vibration systems with nonlinear stiffness and nonlinear damping, two parametric identification methods were proposed. The first method was based on vibration amplitude jumping phenomenon in a nonlinear vibration system, the system was excited with a swept-sine excitation, frequency and amplitude of the amplitude-jumping point’s displacement were obtained through measurement, then the harmonic balance method was used to recognize the nonlinear vibration system’s stiffness and damping. The second method was involved in the time domain transient response of a nonlinear system, Hilbert transformation was used to gain the free vibration response’s amplitude and phase angle of the system, then combining with the analytical solution to the system excited with a transient excitation, the system’s nonlinear stiffness and nonlinear damping were recognized. Taking a vibration isolation system with nonlinear stiffness and nonlinear damping as an example, the two methods mentioned above were verified through numerical simulation. It was shown that the parametric recognition results using these two methods agree well each other. The study results provided a theoretical guide for parametric identification of vibration isolation systems with nonlinear stiffness and nonlinear damping.