With the great development of network technology, the multiserver system gets widely used in providing various of services. And the two-factor authentication protocols in multiserver system attract more and more attention. Recently, there are two new schemes for multiserver environment which claimed to be secure against the known attacks. However, after a scrutinization of these two schemes, we found that (1) their description of the adversary's abilities is inaccurate; (2) their schemes suffer from many attacks. Thus, firstly, we corrected their description on the adversary capacities to introduce a widely accepted adversary model and then summarized fourteen security requirements of multiserver based on the works of pioneer contributors. Secondly, we revealed that one of the two schemes fails to preserve forward secrecy and user anonymity and cannot resist stolen-verifier attack and off-line dictionary attack and so forth and also demonstrated that another scheme fails to preserve forward secrecy and user anonymity and is not secure to insider attack and off-line dictionary attack, and so forth. Finally, we designed an enhanced scheme to overcome these identified weaknesses, proved its security via BAN logic and heuristic analysis, and then compared it with other relevant schemes. The comparison results showed the superiority of our scheme.