We have used different computational methods, including B3LYP, CCSD(T)-F12 and CBS-QB3, to study and compare the addition-elimination reaction of the nitrate radical NO(3) with four sulfur-containing species relevant to atmospheric chemistry: hydrogen sulfide (H(2)S), dimethyl sulfide [(CH(3))(2)S], dimethyl sulfoxide [(CH(3))(2)SO] and sulfur dioxide (SO(2)). We find that the reaction with (CH(3))(2)SO to give NO(2) + (CH(3))(2)SO(2) has a very low barrier, and is likely to be the dominant oxidation mechanism for (CH(3))(2)SO in the atmosphere. In agreement with previous experimental data and computational results, we find that the reaction with H(2)S and SO(2) is very slow, and the reaction with (CH(3))(2)S is not competitive with the hydrogen abstraction route. The differences in reaction energetics and rates between the four species are explained in terms of stabilizing interactions in the transition states and differences in sulfur-oxygen bond strengths.