A simple and economical algorithm is presented for the nonlinear dynamic analysis of networks, with lumped masses on the nodes, bars obeying uniaxial stress-strain laws and no damping. The step-by-step algorithm of the trapezoidal rule is used, combined with the predictor-corrector technique, with only two corrections per step. The prediction of an upper-bound for the eigenfrequencies permits the use of a constant steplength throughout the whole algorithm. An example problem and an error analysis of the algorithm are presented.