In this paper, we analyze the first known provably secure Radio Frequency Identification (RFID) authentication schemes that are designed to provide forward untraceability and backward untraceability: the L-K and S-M schemes. We show how to trace tags in the L-K scheme without needing to corrupt tags. We also show that if a standard cryptographic pseudorandom bit generator (PRBG) is used in the S-M scheme, then the scheme may fail to provide forward untraceability and backward untraceability. To achieve the desired untraceability features, we show that the S-M scheme can use a robust PRBG which provides forward security and backward security. We also note that the backward security is stronger than necessary for the backward untraceability of the S-M scheme.