Abstract. For an ordered hypersemigroup H, we denote by Nthe semilattice congruence on H defined by xNy if and only if the hyperfilters of H generated by the elements x and y coincide. We first prove that this is a complete semilattice congruence on H. Moreover, if H is an ordered hypersemigroup, T a hyperfilter of H and, for a class (z)N of H there is an element in the intersection T \ (z)N, then the class (z)N is a subset of T. From these two statements, the following two important results can be obtained: (1) If H is an ordered hypersemigroup, then each hyperideal of some (z)N-class of H does not contain proper hyperfilters. As a consequence, (2) every prime hyperideal of an ordered hypersemigroup is decomposable into its N-classes