Radio Frequency Identification (RFID) has been widely used in several applications and its security has become a critical issue in this field. So far, several secure schemes have been proposed to authenticate the legitimate reader and tag. However, in these schemes, if the transmitted parameters are lost, the shared counter can become inconsistent. In this condition, the authentication between the reader and the tag will fail and the tag cannot be used in this system anymore. In this thesis, we point out the problem of counter inconsistency in several RFID authentication schemes. Furthermore, we have proposed two schemes to avoid these problems respectively. The first scheme can not only overcome the counter inconsistency problem, but also can improve the search time to find the tag?s identification in the database. In the second scheme, we will propose a lightweight authentication scheme to overcome the asynchronous flaw and withstand the man-in-the-middle attack.