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This paper analyzes the 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 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 component encryptions of the multiple encryption are indistinguishable against chosen plaintext attacks (IND-CPA). We present an extended security notion of sequential multiple encryptions, in which the adversary is allowed to decrypt component encryptions in addition to access to the decryption oracle of the multiple encryption, and show that our constructed scheme satisfies it.