In a world with RFID carriers everywhere, the coexistence proof of multiple RFIDtagged objects shown at the same time and the same place can become a very useful mechanism and be adopted in many application areas such as computer forensics, evidences in law, valuables security, and warning or notification systems, etc. In order to support the correctness of derived proofs, it is necessary to design secure and robust coexistence proofs protocols based on RFID characteristics. In this paper we address the security and privacy requirements for a secure coexistence proofs protocol on RFID tags to defend against tag privacy divulgence, forward secrecy disclosure, denial-of-proof (DoP) attack, and authentication sequence disorder. Along with these design criterions, a recent published secure proofs protocol [11] is evaluated to identify the demand area for security enhancement. To overcome found security weaknesses, tag privacy divulgence and the new known DoP attack in previous proofs schemes, we introduce three anonymous coexistence proofs protocols. According to our security and performance analyses, the proposed protocols possess all required security properties with the same complexity order of the clumping-proofs protocol on computation cost.