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In this paper, a two-user discrete memoryless multiple-access channel (DM-MAC) with correlated channel states, each known at one of the encoders is considered, in which each encoder transmits independent messages and tries to cooperate with the other one. To consider cooperating encoders, it is assumed that each encoder strictly-causally receives and learns the other encoder's transmitted symbols and tries to cooperate with the other encoder by transmitting its message. Next, we study this channel in a special case; we assume that the common part of both states is known at both, hence encoders use this opportunity to get better rate region. For these scenarios, an achievable rate region is derived based on a combination of block-Markov encoding and Gel'fand-Pinsker coding techniques. Furthermore, the achievable rate region is established for the Gaussian channel, and it is shown that the capacity region is achieved in certain circumstances.