Abstract: We extend the sequential model for dynamic programming to a parallel model. We propose three general parallel dynamic programming algorithms for pipeline and ring networks for multistage automatons. The study of the optimality lead us to the introduction of two new classes of multistage automatons: nondecreasing automatons and strongly increasing automatons. As an example, this parallel dynamic programming approach is applied to the single resource allocation problem. Results both for transputer networks and for local area networks using PVM are reported. The experience proves that the proposed algorithms can be easily and efficiently implemented. Furthermore, these procedures constitute a suitable kernel to build general parallel tools for dynamic programming.