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The problem of minimax robust coding for classes of channels with uncertainty in their statistical description is addressed. Specific consideration is given to: 1) discrete memoryless channels with uncertainty in the probability transition matrices; 2) discrete-time stationary Gaussian channels with spectral uncertainty; and to uncertainty with classes determined by 2-alternating Choquet capacities. Both block codes and convolutional codes are considered. A robust maximum-likelihood decoding rule is derived; the rule guarantees that, for all channels in the uncertainty class and all rates smaller than a critical rate, the average probability of decoding error for the ensemble of random block codes and the ensemble of random time-varying convolutional codes converges to zero exponentially with increasing block length or constraint length, respectively. The channel capacity and cut-off rate of the class are then evaluated.