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The user authentication mechanism is an important part of the network security to protect unauthorized access of a networked system. Based on cryptographic techniques, several schemes have been proposed in the literature for ID-based authentication schemes with smart cards. In 2004, Das et al. propose a scheme for a dynamic ID-based remote user authentication using smart cards. In this paper, we present some security flaws on their scheme. Further, we propose dynamic ID-based and ID-based remote user authentication schemes using smart cards those can eliminate the flaws those are found in their scheme. Moreover, our schemes provide the users to choose and change their passwords by their own choices. Further, our schemes provide better trade-off among efficiency, flexibility and security than the schemes previously published.