In this paper, we analyze sequential bankruptcy problems, which generalize bankruptcy problems. They cover the problems of sharing water in a transboundary river and of allocating expedition rewards in projects. We propose the upwards mechanism for generalizing rules for bankruptcy problems to rules for sequential bankruptcy problems. Further, we characterize the upwards constrained equal awards, the upwards constrained equal losses, and the upwards proportional rules on the basis of upwards composition and upwards path independence.