In this paper we describe the non-linearity of the NO-H-2 reaction over Rh surfaces. Rate oscillations have been observed over a stepped (111) surface with (100) steps, (Rh(533) at low pressures (10(-4) Pa) below 500 K, while no oscillations could be observed under these conditions over a Rh(100) surface and a stepped (100) surface with (ii I) steps, Rh(711). The thermal stability of the N atoms formed during the reaction explains the observed structure sensitivity. Moreover, the results suggest that diffusion of N atoms is needed to synchronise the rate oscillations, a process that is absent on Rh(100) and Rh(711).