Abstract: The fluid viscous dampers (FVDs) have received great appeals in engineering applications. Generally, the output force against the damper velocity is a nonlinear function in the form of fractional-power law. The usual damping exponent in practical applications is usually 0.3-0.5, within which the traditional time-integration methods for nonlinear analysis, such as the Newmark formula and the newly developed KR-α formula, etc., would suffer from instability and spurious numerical pulses; whereas the conventional energy-equivalence based formulas suffers from iteration and relatively low accuracy. In the present paper, the stiff properties of the viscously damped nonlinear systems are systematically analyzed. Then the backward difference formulas (BDFs) are introduced. The advantages of the BDFs over the above mentioned formulas are demonstrated through comparative studies. The accuracy, stability and efficiency of these formulas are examined. Numerical results reveal that the BDFs operate well in guaranteeing the stability of the algorithm, and in gaining high accuracy of solutions of stiff systems.