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The multiple-access wiretap channel (MAC-WTC) with common channel state information (CSI) at the encoders is studied, where two transmitters wish to send their confidential messages (no common message) to a legitimate receiver, while keeping a wiretapper as ignorant of the confidential messages as possible. Meanwhile, the channel is controlled by CSI, and it is available at the transmitters in a non-causal manner or causal manner. This model can be viewed as a MAC extension of the WTC with CSI. Both the situation that the encoders can cooperate with each other and the situation that cooperation is not allowed between the encoders are investigated. More specifically, first, the cooperative MAC-WTC with common CSI at the encoders is investigated, inner bounds on the secrecy capacity regions are provided for both non-causal and causal manners. Secondly, the non-cooperative MAC-WTC with common CSI at the encoders is investigated, and also provide inner bounds on the secrecy capacity regions for both non-causal and causal manners. Finally, by calculating the binary examples, the authors find that the cooperation between the encoders helps to obtain a larger secrecy rate region, that is, cooperation enhances the security of the MAC-WTC with common CSI at the encoders.