Abstract: Constraint propagation is one of the key elements of constraint programming. After presenting supporting theories of constraint propagation for cumulative scheduling problems (CuSP), the authors propose a constraint propagation algorithm in which both precedence constraints and activity time bound constraints are taken into consideration. By citing two sets of benchmark problems of PSPLIB to test the algorithm, experimental results show that the new algorithm outperforms existing constraint propagation algorithms for the testing problems. Moreover, the new algorithm and the energetic reasoning algorithm may complement each other. A hybrid one of the two algorithms is promising.