The problem of minimax robust coding for classes of multiple-access channels with uncertainty in their statistical description is addressed. We consider1)discrete memoryless multiple-access channels with uncertainty in the probability transition matrices and2)discrete-time stationary additive Gaussian multiple-access channels with spectral uncertainty. The uncertainty is modeled using classes determined by two-alternating Choquet capacities. Both block codes and tree codes are considered. A robust maximum-likelihood decoding rule is derived which guarantees that, for ali two-user channels in the uncertainty class and all pairs of code rates in a critical rate region, the average probability of decoding error for the ensemble of pairs of random block codes and the ensemble of pairs of random tree codes converges to zero exponentially with increasing block length or constraint length, respectively. The channel capacity and cutoff rate regions of the class are then evaluated.