Pathological neural activity in subthalamic nucleus (STN) is closely related to the symptoms of Parkinson's disease. Local field potentials (LFPs) recordings from subthalamic nucleus show that power spectral peaks exist at tremor, double tremor and tripble tremor frequencies, respectively. The interaction between these components in the multi-frequency tremor may be related to the generation of tremor. To study the linear and nonlinear relationship between those components, we analyzed STN LFPs from 9 Parkinson's disease patients using time frequency, cross correlation, Granger casuality and bi-spectral analysis. Results of the time-frequency analysis and cross-frequency correlation analysis demonstrated that the power density of those components significantly decreased as the alleviation of tremor and cross-correlation (0.18~0.50) exists during tremor period. Granger causality of the time-variant amplitude showed stronger contribution from tremor to double tremor components, and contributions from both tremor and double tremor components to triple tremor component. Quadratic phase couplings among these three components were detected by the bispectral approaches. The linear and nonlinear relationships existed among the multi-components and certainly confirmed that the dependence cross those frequencies and neurological mechanism of tremor involved complicate neural processes.