As shown by Hořava and Witten, there are gravitational anomalies at the boundaries of M 10 × S 1/ Z2 of 11-dimensional supergravity. They showed that only 10-dimensional vector multiplets belonging to the E8 gauge group can be consistently coupled to this theiry. Thus, the dimensional reduction of this theory should be the low-energy limit of the E8 × E8 heterotic string. Here we assume that M-theory is a theory of supermembranes which includes twisted supermembranes. We show that for a target space M 10 × S 1/ Z2, in the limit in which S 1/ Z2 in small the effective action is the E8 × E8 heterotic string. We also consider supermembranes on M 0 × S 1 × S 1/ Z2 and find the dualities expected from 11-dimensional supergravity on this manifold. We show that the requirements for world-sheet anomaly cancellations at the boundaries of the world-volume action are the same requirements imposed on the Hořava-Witten action.