The influence of zeolite support materials and their impact on CH4 oxidation activity was studied utilizing Pd supported on H-beta and H-SSZ-13. A correlation between CH4 oxidation activity, Si/Al ratio (SAR), the type of zeolite framework, reduction-oxidation behaviour, and Pd species present was found by combining catalytic activity measurements with a variety of characterization methods (operando XAS, NH3-TPD, SAXS, STEM and NaCl titration). Operando XAS analysis indicated that catalysts with high CH4 oxidation activity experienced rapid transitions between metallic- and oxidized-Pd states when switching between rich and lean conditions. This behaviour was exhibited by catalysts with dispersed Pd particles. By contrast, the formation of ion-exchanged Pd2+ and large Pd particles appeared to have a detrimental effect on the oxidation-reduction behaviour and the conversion of CH4. The formation of ion-exchanged Pd2+ and large Pd particles was limited by using a highly siliceous beta zeolite support with a low capacity for cation exchange. The same effect was also found using a small-pore SSZ-13 zeolite due to the lower mobility of Pd species. It was found that the zeolite support material should be carefully selected so that the well-dispersed Pd particles remain, and the formation of ion-exchanged Pd2+ is minimized.