In an internet environment, such as UNIX, a remote user has to obtain the access right from a server before doing any job. The procedure of obtaining acess right is called a user authentication protocol. User authentication via user memorable password provides convenience without needing any auxiliary devices, such as smart card. A user authentication protocol via username and password should basically withstand the off‐line password guessing attack, the stolen verifier attack, and the DoS attack. Recently, Peyravian and Zunic proposed one password transmission protocol and one password change protocol. Later, Tseng et al. (2001) pointed out that Peyravian and Zunic's protocols can not withstand the off‐line password guessing attack, and therefore proposed an improved protocol to defeat the attack. Independently, Hwang and Yeh also showed that Peyravian and Zunic's protocols suffer from some secury flaws, and an improved protocol was also presented. In this paper, we show that both Peyravian and Zunic's protocols and Tseng et al.'s improved protocol are insecure against the stolen verifier attack. Moreover, we show that all Peyravian and Zunic's, Tseng et al.'s, and Hwang and Yeh's protocols are insecure against DoS attack.