We consider a two-user state-dependent multiaccess channel in which the states of the channel are known, causally or only strictly causally, at both encoders, but not at the decoder. Both encoders transmit a common message and, one of the encoders also transmits an individual message. We study the capacity region of this communication model for both causal and strictly causal settings. For the model with causal states, we find an explicit characterization of the capacity region in the discrete memoryless case. For the model with strictly causal states, we establish inner and outer bounds on the capacity region. The outer bound is non-trivial, has a relatively simple form and has the advantage of incorporating only one auxiliary random variable. In particular, it suggests that there is none, or at best only little, to gain from having the encoder that transmits both messages also sending an individual description of the state to the receiver, in addition to the compressed version that is sent cooperatively with the other encoder. The results shed more light on the utility of delayed channel state information for increasing the capacity region of multiaccess channels; and tie with some recent progress in this framework.