Catalytic membrane reactors have the potential to render the process of oxidative coupling of methane economically viable. Here, the results from operando XRD-CT studies of three different catalytic membrane reactors, employing BaCo_0.4Fe_0.4Zr_0.2O_3-δ (BCFZ) and La_0.6Sr_0.4Co_0.2Fe_0.8O_3-δ (LSCF) perovskite membranes with Mn-Na-W/SiO₂ and La-promoted Mn-Na-W/SiO₂ catalysts, are presented. It is shown that synchrotron X-ray tomographic diffraction imaging allows the extraction of spatially-resolved diffraction information from the interior of these working catalytic membrane reactors and makes it possible to capture the evolving solid-state chemistry of their components under various operating conditions (i.e. temperature and chemical environment).