Since network services are provided cooperatively by multiple servers in the Internet, the authentication protocols for multiserver architecture are required by Internet-based services, such as online game, online trade and so on. Recently, Li et al. analyzed Lee et al.'s protocol and proposed an improved dynamic identity based authentication protocol for multi-server architecture. They claimed that their protocol provides user's anonymity, mutual authentication and the session key agreement against several kinds of attacks. In this paper, a cryptanalysis on Lee et al.'s scheme shows that Lee et al.'s protocol is also vulnerable to malicious server attack, stolen smart card attack and leak-of-verifier attack. Moreover, Li et al.'s improved protocol is also vulnerable to all these attacks. Further cryptanalysis reveals that Li et al.'s improved protocol is susceptible to collusion attack.