The mechanisms of the reactions of dimethylsulfide, (DMS) and dimethylselenide (DMSe) with peroxynitrite anion, ONOO-, and peroxynitrous acid, HOONO, were studied at the B3LYP/6-311 + G(d,p) level of theory. It was shown that the gas-phase reactions with ONOO- proceed via an O-atom (O-3) transfer (two-electron oxidation) mechanism and produce the corresponding oxides (DMSO and DMSeO, respectively) and NO2- anion. The rate-determining barrier, the O-O bond cleavage, is found to be higher by 6-7 kcal/mol for DMS than for DMSe, indicating that DMSe is more reactive toward ONOO- than DMS. The inclusion of solvent effects decreases the rate-determining barrier and makes it < 13.5 kcal/mol in aqueous solution for the DMS reaction. These data indicate that neither DMS nor DMSe catalyze the direct peroxynitrite - nitrate isomerization. It was shown that the reaction of DMS with cis-HOONO might proceed via two distinct pathways, stepwise and concerted, and is much faster than that with ONOO-. The stepwise pathway starts with homolysis of the HO-ONO bond to discrete HO. and ONO.\ radicals, which then coordinate to DMS and produce the (CH3)(2)S(OH)(NO2) intermediate product. This product undergoes further transformations via two different pathways: (a) a barrierless and endothermic pathway leading to the (CH3)(2)S(OH)(.) and N02* radicals, and (b) an exothermic H-atom transfer pathway forming DMSO and HONO via a barrier at the TS2(H-transfer) transition state. The DeltaH(AG) values of the rate-determining steps of these two pathways are 24.3 (11.0) and 11.5 (13.1) kcal/mol, respectively, in the gas phase. The concerted pathway proceeds with an O-O bond cleavage barrier of 6.1 (6.3) kcal/mol and leads to DMSO and HONO. It is predicted that the reaction of DMS with HOONO in the gas phase most likely proceeds via the stepwise (one-electron oxidation) pathway only after including entropy effects. However, in the solution phase the stepwise and concerted pathways will effectively compete with each other.