We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non-additive (as the relations representable by a probability) and also not ``partially monotone" (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means of ``dual" conditions given on the contrary events, like in the numerical case.