Alumina-supported mono- and bimetallic cobalt (Co) and palladium (Pd) monolithic catalysts were prepared and tested for methane catalytic combustion. The activity test showed that the catalyst containing 0.1 wt % Pd and 0.25 wt % Co was the most promising, with a high activity that did not decline with time on stream. With the aim to explain the relationship between activity stability and structure, the catalysts were characterized by scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and temperature-programmed oxidation (TPO) techniques. The high stability displayed by the bimetallic catalysts is attributed to the influence of Co upon hindering the decomposition of PdO into metallic palladium, as a consequence of the increase in oxygen mobility in the spinel phase of cobalt oxides. The intrinsic kinetics of the methane oxidation reaction over various Pd-Co mono- and bimetallic catalysts has been measured in a fixed-bed reactor in the absence of internal and external diffusions, and the 0.1% Pd-0.25% Co/gamma-Al2O3 catalyst exhibited the lowest activation energy. This work combines the advantages of the Pd-Co bimetallic catalyst with the monolithic structure.