Palladium supported on Si-stabilised alumina has been demonstrated to be an active and durable catalyst for the combustion of methane. Si is more effective in stabilising alumina than La or Ba when the elements are added through an impregnation technique. Multiple stabilisation with combinations of La, Ba and Si does not increase further the stability against sintering. The stability increases logarithmically with the amount of Si added (0.5-8 atomic%). The rate of sintering is not affected by an increase of the water vapour content of the atmosphere from 1 to 20 vol.%. Doping palladium with rhodium or platinum increases the activity of the catalyst for methane combustion. The high-temperature stability of pure Pd is however superior to the stabilities of the Rh- and Pt-doped catalysts. Addition of La or Ce to the Pd-catalyst increases its stability against thermal deactivation but leads to an overall decrease in activity. The activity of the as-prepared catalysts are affected by the Pd-content below a value corresponding to 5% of the monolayer capacity. Thermally deactivated catalysts show a stronger activity dependence of the Pd-content than as-prepared catalysts. The combustion reaction is first order with respect to methane and zero-order with respect to oxygen (>2 vol.% of oxygen). Carbon dioxide has no inhibitory effects on the combustion. The activity of the Pd-catalyst is decreased by a factor of 5 through deactivation at 1473 K for 768 h. The decrease in activity is linearly correlated to the decrease in specific surface area.