Periodic trends in the decomposition of NO and its reduction to N2 and NH3 by CO and H2 on transition metal surfaces have been analyzed theoretically using the bond order conservation Morse potential (BOCMP) method. The analysis is based on calculations of the energetics, the reaction enthalpies DEKTAH and activation barriers DELTAH*, of elementary steps thought to comprise the mechanisms of the NO transformations. As the periodic series, the close-packed surfaces Pt(111), Rh(111), Ru(001), and Re(001) were chosen. The calculated heats of chemisorption Q Of NH3, NH2, NH, NO, H2O and OH are in good agreement with experiment. The activation barriers for dissociation of NO from a chemisorbed state, DELTAE(NOs)* were found to decrease in the order Pt > Rh > Ru > Re. For reasonable values of Q(N) and Q(O), in the zero-coverage extreme these activation barriers were calculated to be much smaller than the relevant heats of chemisorption Q(NO), so that dissociation of No upon heating is projected for all the surfaces studied with the possible exception of Pt(111). The presence of adsorbed N(s) and O(s) atoms may dramatically increase the values of DELTAE(NOs)*, for example, from 7-9 to 24-27 kcal/mol for Rh(100) and Rh(100)c(2 x 2)O,N, respectively. This sensitivity of the values of DELTAE(NOs)* to NO(s) coverage may explain the diversity of experimental results obtained for different coverages (exposures) and temperatures even for the same single crystal face. The anisotropy of the values of Q(X) (X = NO, N, O) for different surfaces and possible reconstructions of these surfaces also contribute to the balance between dissociation and desorption of NO. Of the two channels for recombinative desorption of N2, 2N(s) --> N2,g and N(s) + NO(s) --> N2,g + O(s) the latter has the smaller activation barrier. Because the N2 formation barriers rapidly increase in the order Pt approximately Rh much less than Ru much less than Re, Rh or Rh-Pt surfaces are projected to be the most efficient catalysts for NO reduction by CO (to N2 and CO2). Similarly, Pt surfaces are projected to be the most efficient catalysts for NO reduction by H-2 (to NH3 and H2O). The general mechanistic picture emerging from the BOCMP analysis concurs with experimental data. Some apparent inconsistencies, particularly concerning the dissociation of NO, are discussed and some model conclusions to be verified by future experiments are noted.