The moduli spaces of p-divisible groups are introduced by Rapoport and Zink which are formal schemes over the ring of integers of some non-archimedean field.They are local analogue of Shimura varieties.We will determine the set of geometrically connected components of the generic fiber of Rapoport-Zink spaces with level structures as rigid analytic spaces.The talk is partly based on a joint work with Mark Kisin and Eva viehmann.