Ce0.5Zr0.5O2-supported palladium catalysts were prepared and used for CO and methane oxidation. The redox behaviour of these catalysts was investigated by using H-2-TPR and CO-TPR. The shape and temperature of TPR peaks depend on the nature of reducing agent. Two peaks (alpha(1) and gamma) were observed when H-2 was used as reducing agent for the fresh catalyst, while three peaks (alpha', beta' and gamma') were observed when CO was used as a reducing agent. The addition of a noble metal effectively promotes the reduction of Ce0.5Zr0.5O2 support, which is attributed to hydrogen spillover. After re-oxidation treatments, the PdO reduction process splits into two peaks (alpha(1) and alpha(2)). On the basis of the catalytic activity and CO-TPR results, the activity of CO oxidation is related to the finely dispersed PdO, while the activity of methane oxidation is related to the large PdO particles.