Abstract: Uncertainty inherited in the parameters of multibody systems will induce significant deviation on the dynamic responses. The interval analysis method, which only need the information of lower and upper bounds of the interval uncertain parameters, can efficiently consider uncertainties in the dynamics analysis of multibody systems. The bounds of responses obtained by the CIM (Chebyshev interval method) for multibody systems in the presence of interval uncertainty would deteriorate with the increase of time history. To circumvent this problem, two novel methods CIM-HHT (Hilbert-Huang transform) and CIM-LMD (local mean decomposition), which combine signal decomposition technique and Chebyshev polynomials, are developed in this paper to accurately envelope the long period interval responses of system under interval uncertainty. The HHT and LMD are combined, respectively, with the Chebyshev polynomials to approximate the instantaneous amplitude and phase obtained by signal decomposition. HHT and LMD can decompose the multicomponent responses of multibody system into the sum of several monocomponent and a trend component. Then, the instantaneous amplitude and instantaneous phase of the monocomponent, and the trend component can be employed to construct corresponding surrogate model by the Chebyshev polynomials, respectively. Based on the surrogate models for the instantaneous amplitude, instantaneous phase and trend component, the coupling entire surrogate model for the system can be established and the upper bound and lower bound of the system responses can be calculated subsequently. To verify the accuracy and effectiveness of the proposed methods, a simple pendulum and a crank slider under interval uncertainty are presented. Numerical results demonstrated that the CIM-HHT and CIM-LMD present desirable computational accuracy in the procedure of long period interval dynamic analysis of multibody systems. Furthermore, compared with CIM-HHT, the CIM-LMD is characterized with weaker end effect and high computational accuracy in the long period interval dynamic analysis of multibody systems.