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This paper deals with the long-term dynamic behaviors of a complex rotor-bearing system with multi-degrees-of-freedom and nonclosed form of the bearing forces. Since nonanalytical bearing forces can be available, to increase the numerical accuracy and decrease the CPU time, a new method is presented to calculate the Jacobians of the bearing forces and bearing forces themselves. The algorithm is concise and the computing efforts spent on the Jacobians are very small compared to spend on the bearing forces themselves. In terms of the feature that the nonlinear bearing forces act on the system individually, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease the computing time for the system analysis. The numerical schemes of this study are applied to a rotor system with multi-rigid disks and two elliptical bearing supports. The numerical results reveal very rich and complex nonlinear behavior of the system. [S0021-8936(00)00802-3]