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....