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A new higher order explicit one step scheme is presented for use in the,solution of a certain class of nonlinear problems in structural dynamics. The generalized scheme covers some recently developed multistep algorithms as well as some new one step methods with improved numerical properties. A weighted residual approach is used which contains new aspects for design of single step algorithms. Accuracy and stability are investigated for linear and non-linear systems. Algorithms with higher accurary than the central difference method are developed and optimized to minimize the reduction in the stability limit.