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We consider a memoryless multiple-access channel (MAC) that is governed by two independent memoryless state sequences, each of which is revealed to a different encoder in a strictly causal or causal way. The special case where one of the state sequences is deterministic (null) corresponds to an MAC governed by a single state that is revealed to only one of the encoders. We show that, even in the strictly causal case, the state information at the encoders can increase the capacity region. It cannot, however, increase the sum-rate capacity. We provide general inner and outer bounds on the capacity region, and we also study a Gaussian example where they coincide. We show that in the causal case, naïve Shannon strategies may be suboptimal.