Let [Formula: see text] be the set of all nonempty subsets of a ternary semigroup [Formula: see text]. Then [Formula: see text] is a ternary semigroup with respect to the ternary multiplication defined by [Formula: see text] for all [Formula: see text]. If [Formula: see text] and [Formula: see text] are isomorphic ternary semigroups, then the corresponding power ternary semigroups [Formula: see text] and [Formula: see text] are obviously isomorphic. It is quite natural to ask whether the converse is true, i.e. is it true that for any ternary semigroups [Formula: see text] and [Formula: see text], [Formula: see text] implies that [Formula: see text]? If the class [Formula: see text] of algebra has this property, we say that [Formula: see text] is a globally determined class. In this paper, we provide some class of globally determined ternary semigroups. We show that all ternary semigroups are not globally determined but some special classes of ternary semigroups are globally determined. We show that the class of finite left (right) zero ternary semigroups, ternary groups and principal ideal (P. I.) ternary semigroups are globally determined but the class of involution ternary semigroups is not globally determined.