Most of the fair exchange protocols use a trusted third party (TTP) or an arbitrator T who can be called upon to handle disputes between two business parties. However, it is practically hard to find entities to act as TTP. In this paper, two fair E-Commerce protocols, without any TTP, based on concurrent signatures are presented. One protocol aims at delivering physical goods and the other is designed for digital goods. Finally, the fairness and security of these two protocols are discussed.