Neutroosphy is the study of neutralities founded by Smarandache in 1998. Starting with a partial order on a NeutroSemihypergroup, the authors get a NeutroHyperstructure. If it satisfies the conditions of NeutroOrder, it becomes a NeutroOrderSemihypergroup. This chapter introduces the field of NeutroOrderHyperstructures by considering a special class of it: NeutroOrderSemihypergroups. Some new definitions are provided, some properties of the new defined concepts are investigated, and illustrative examples are presented.