The energetics of O-H, N-H, and C-H bond cleavage on clean and (low-coverage) oxygen-preadsorbed metal surfaces has been analyzed using the BOC-MP (bond-order-conservation-Morse-potential) method. The molecules in question included CH3OH, HCOOH, and NH3, adsorbed on Ag(111), Cu(111), Ni(111), W(110), and CH4 adsorbed on Ni(111) and Ni(100). The reaction enthalpies, DELTA-H, and the activation energies, DELTA-E*, have been calculated for a variety of elementary steps corresponding to the direct and oxygen-assisted cleavage of X-H bonds (X = O, N, C). For the O-H and N-H bonds, the presence of preadsorbed oxygen always decreases the values of DELTA-H and DELTA-E* for Ag(111), but increases them for W(110). For Cu(111) and Ni(111), the changes in DELTA-H and DELTA-E* are less uniform but, as a whole, Cu(111) resembles Ag(111), whereas Ni(111) is closer to W(110). In other words, the effect of preadsorbed oxygen at low coverages on the O-H and N-H bond cleavage is projected to be reversed along the series Ag, Cu, Ni, W, from facilitating X-H bond cleavage on the least active metals such as Ag (or Au), to inhibiting this process on the most active metals, such as W (or Mo). The presence of preadsorbed oxygen on Ni(111) and Ni(100) is detrimental to the cleavage of C-H bonds in CH4. The BOC-MP model projections are in broad agreement with experimental observation.