We present a molecular dynamics simulation scheme which allows to speed up molecular dynamics simulations by linear prediction of force time series. The explicit calculation of nonbonding forces is periodically replaced by linear prediction from past values. Applying our method to liquid oxygen consisting of flexible molecules we obtained real speedups between 5.4 and 6.5, compared to conventional molecular dynamics simulations. Here only the bond-stretching forces were calculated at each time step. We demonstrate that essential dynamical quantities, such as the mean-square displacement and the velocity autocorrelation function, are preserved. (C) 2003 American Institute of Physics.