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An important challenge regarding peer's trust valuation in peer-to-peer (P2P) networks is how to cope with such problems as dishonest feedbacks from malicious peers, collusions and complex strategic frauds, which cannot be effectively tackled by the existing solutions. Thus, a reputation-based distributed trust management model for P2P networks, named RATM for short, is proposed to quantify and evaluate the trustworthiness of peers. In RATM, the metric of time zone is used to describe the time property of the transaction experiences and recommendations; the peer trust value, the short trust value and the long trust value are applied to express accurately the final trust level of peers. Moreover, the trust deviation value and the trust abuse value are introduced to depict the above several trust metrics. Theoretical analyses and simulation experiments demonstrates that, RATM has advantages in combating various dynamic malicious behaviors such as dishonest feedbacks and strategic malicious attacks, over the current trust model, and shows more effectiveness and stronger dynamic adaptability.