Properties of sup-∗ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider sup-∗ powers of fuzzy relations under diverse assumptions about ∗ operation. At first, we remind fundamental properties of sup-∗ composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined. Finally, particular properties of fuzzy relations on a finite set are presented.