Abstract: In wireless communications, various anonymous mutual authentication schemes use public key cryptosystems to provide secure roaming service but are not computationally efficient. Guo et al., first, proposed an efficient mutual authentication protocol providing user anonymity and using smart cards but this scheme has security weaknesses. Liu et al. attempted to address this by proposing a mutual authentication scheme in wireless communications with anonymity for roaming service with smart cards in wireless communications but this scheme still has security vulnerabilities. The present study demonstrates security problems of mutual authentication scheme: it is vulnerable to offline password (and identity) guessing attack does not provide perfect forward secrecy is vulnerable to DoS attack and provides weak anonymity.