This paper analyzes security of sequential multiple encryptions based on asymmetric key encryptions, and shows that a sequential construction of secure multiple encryptions exists. The sequential multiple encryption scheme can be proved to be indistinguishable against chosen ciphertext attacks for multiple encryptions (IND-ME-CCA), where the adversary can access to the decryption oracle of the multiple encryption, even when all the underlying encryptions of the multiple encryption are indistinguishable against chosen plaintext attacks (IND-CPA). We provide an extended security notion of sequential multiple encryptions, in which the adversary is allowed to access decryption oracles of the underlying encryptions in addition to the multiple encryption, and show that our constructed scheme satisfies the security notion when all the underlying encryptions are indistinguishable against chosen ciphertext attacks (IND-CCA).