Abstract: The direct time integration methods for nonlineardynamic equations are based on a relationship of state variablesbetween the time of t and t+\Delta t, and the nonlinear dynamic equationscan be converted into a set of nonlinear algebraic equations,to be solved with Newton-Raphson or BFGS iterations during eachtime increment. The composite implicit time integration methodproposed by K. J. Bathe is deduced for dynamic equations including nonlineardamping, in which the velocity is taken as the basic variable in this paper.Sdof system with fluid viscous dampers is taken as an example, and Fortranprograms are developed according to above iteration procedure and Newmar k-\beta algorithm based on BFGS iteration for the Sdof system. Resultsare compared with that of Adina, and the accuracy is valieated.