The thermal decomposition of azomethane on clean and oxygen-covered Rh(111) has been investigated using a combination of temperature-programmed reaction, high-resolution electron energy loss and Fourier transform infrared spectroscopies. On clean Rh(111), azomethane adsorbs molecularly in the trans conformation and is stable on the surface up to 250 K. Above 300 K azomethane reacts exclusively by nitrogen-nitrogen bond scission, yielding gaseous HCN, H-2, N-2, and C2N2 HCN is evolved in four peaks between 300 and 600 K. Adsorbed CN reacts via two competing pathways : recombination to cyanogen and dissociation to adsorbed N, which recombines to gaseous N-2 above 600 K. Adsorbed oxygen inhibits N=N bond breaking, leading to the carbon-nitrogen bond dissociation products CO, CO2, and formaldehyde. On Rh(111)-p(2 x 1)-O (theta(o) = 0.5 monolayers), similar to 77% of the azomethane reacts via carbon-nitrogen bond scission. The C-N bond breaking is proposed to occur via adsorbed CH2-=N-N-CH3, based on vibrational and temperature-programmed reaction data. Subsequent carbon-nitrogen bond cleavage yields gaseous N-2 and is proposed to be accompanied by formation of transient CH2 and CH3, which add to surface oxygen. Methyl would add to oxygen to form methoxy, which rapidly dehydrogenates to produce CO, CO2, and H2O. Gaseous formaldehyde is proposed to form from addition of CH2 to oxygen followed by rapid desorption. The variation in the product distributions with oxygen coverage indicates a subtle interplay between the inhibition of nitrogen-nitrogen and C-H bond cleavage by oxygen and is cast in a general framework for hydrocarbon oxidation on Rh surfaces.