A combination of first-principles thermodynamics and density functional theory (DFT) was applied for the prediction of sulfur-poisoned monomeric Cu/Fe species formed in the SSZ-13 catalyst framework under selective catalytic reduction (SCR)-relevant conditions in the presence of sulfur dioxide, ammonia, oxygen, and water. Differences in fresh and sulfur-poisoned species were found for Cu- and Fe-SSZ-13 catalysts containing one Al (1Al sites) or two Al (2Al sites) in 6-membered rings (6MRs) or 8-membered rings (8MRs). The impact of ammonia concentration during low-and high-temperature sulfur-poisoning on Cu- and Fe-speciation was also investigated. SCR-relevant concentrations of ammonia in the gas mixture led to the formation of ammonium sulfates over copper in 2Al and 1Al sites of Cu-SSZ-13, while bisulfate and sulfuric acid species were predicted at these copper sites either in the absence of ammonia or at negligible concentrations of ammonia during low- and high-temperature poisoning. The absence of ammonia in the gas mixture led to the formation of iron-bisulfates at 2Al sites of Fe-SSZ-13 during low- temperature poisoning, while the formation of ammonium sulfates was favorable under SCR-relevant conditions. In contrast to the facile formation of ammonium sulfates at copper sites of Cu-SSZ-13, only ammonium-free iron-sulfates formed at 1Al sites in Fe-SSZ-13 under realistic operational conditions. The regeneration of 2Al sites of Cu-SSZ-13 was predicted to occur at higher temperatures compared to 2Al sites in Fe-SSZ-13, whereas the opposite was predicted for 1Al sites. The analysis of fresh and regenerated Cu/Fe species was carried out as well. These theoretical results on model catalysts provide a first step in the understanding of sulfur-poisoning in Fe-SSZ-13 catalysts, supporting further experimental investigations to improve NH3-SCR catalysts for meeting future emission standards.