We study the state-dependent multiple access channel (MAC) with causal side information at the encoders. The channel state consists of two independent components, S1 and S2, available at Encoder 1 and Encoder 2, respectively. The problem where the state is available at only one of the encoders is a special case . We consider two scenarios. In the first, the states are available at the encoders in a strictly causal manner. We derive an achievable region, which is tight for a Gaussian MAC where the state sequence comprises the channel noise and is available at one of the encoders only. In the second scenario the state sequence is available to the encoders in a causal manner, as in Shannon's model. A simple extension of the previous result to Shannon strategies yields an achievability result. Our region contains as a special case the naïve rate region obtained when each of the users applies Shannon strategies. In some cases the inclusion is strict.