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Recently, Elliptic Curve Cryptosystem (ECC) based remote authentication scheme has been used for mobile devices. For instance, Yang and Change proposed an ID-based remote mutual authentication with key agreement scheme for mobile devices on Elliptic Curve Cryptosystem in 2009. However, in this paper, we found that their scheme still is vulnerable to insider attack and impersonation attack. Therefore, we proposed an advanced ECC ID-Based remote mutual authentication scheme for mobile devices to solve the issues. Furthermore, we analyzed our scheme to show that our scheme is more secured to authenticate users and remote servers for mobile devices.