TDS, XPS, and XAES were used to examine the reaction of S-2 gas with NM/Mo(110) (NM = Cu or Ag). On these surfaces S-2 dissociates into atomic S at 300 K. At submonolayer coverages (theta(s) + theta(NM) < 1 ML), S and Cu or Ag do not react to form noble-metal sulfides on top of Mo(110). Instead, the S and noble-metal adatoms compete for making bonds with the Mo(110) substrate. On the average, each S adatom diminishes the ability for bimetallic bonding of a minimum of three Mo surface atoms. At 0.4 < theta(s) < 0.8 ML, the weakening of the Mo-Cu and Mo-Ag bonds is very significant (>5 kcal/mol), and the noble-metal adatoms form 3D clusters on the Mo(110) surface. The exposure of NM/Mo(110) surfaces to large amounts of S-2 gas (theta(s) > 1 ML) at 300 K produces noble-metal sulfides (CuSx or AgSy) and chemisorbed sulfur, without forming molybdenum sulfides. The sulfidation of molybdenum occurs after exposing NM/Mo(110) surfaces to S-2 at 600-700 K. Cu and Ag promote (or catalyze) the formation of molybdenum sulfides. By comparing the results for the S-2/NM/Mo(110) systems with those reported for S-2/NM/Pt(111) systems, it is found that the "promotional effect" of a noble metal on the rate of sulfidation of a transition metal depends on (a) the ability of the noble metal to dissociate S-2, (b) the thermochemical stability of the transition-metal sulfide (which makes the process "downhill"), and (c) the atom-atom attractive interactions within the lattice of the transition metal (which make the process "uphill").