Most password-authenticated key exchange schemes in the literature provide an authenticated key exchange between a client and a server based on a pre-shared password. With a rapid change in modem communication environments, it is necessary to construct a secure end-to-end channel between clients, which is a quite different paradigm from the existing ones. In this paper we propose a new framework which provides a password-authenticated ky exchange between clients based only on their two different Passwords without my Pre-shared secret, so called Client-to-Client Password-Authenticated Key Exchange(C2C-PAKE). Security notions and types of possible attacks are newly defined according to the new framework We prove our scheme is secure against all types of attacks considered in the paper. Two secure C2C-PAKE schemes are suggested, one in a cross-realm setting and the other in a single-sorrel setting.