In this work we studied the effect of acidity and of oxygen on the reduction of NO with CH4 on Pd sulphated zirconia and alumina supports under reducing and oxidizing feed conditions. The acidity of sulphated zirconia (SZ) is higher than sulphated alumina (SA). The surface acids are Lewis sites and are responsible for the NO dissociation. The introduction of Pd affects the acidity and surface area. The conversion of NO is higher on the Pd/SA than on Pd/SZ catalyst under reducing condition. The addition of O-2 increased the oxidation of methane. The NO molecules are adsorbed dissociatively into N and O species. The higher acidity inhibits the dissociation and reaction over the metallic Pd particles. Oxygen favored the oxidation of Pd particles and influences negatively the NO conversion.