Parallel algorithms for critical path problems are studied. A sensitization criterion is presented. Based on this sensitization criterion, the DT-algorithm, which is a variation of the D-algorithm with stable time range of signals also taken into consideration, is developed. It is especially suitable to determine the sensitizability of a given path in a parallel processing environment. The authors discuss a parallel implementation of the critical path algorithm on a shared-memory multiprocessor. The experimental results show that a reasonable speed-up can be obtained.