A method of high-performance dry reforming of methane into syngas at temperatures below 650 °C on membrane catalytic systems was proposed. The membrane catalytic systems consist of porous inorganic membrane-supports, prepared by self-propagating high-temperature synthesis and modified by nanosized metallocomplex components, which are uniformly distributed inside membrane pores. The influence of the composition of the supported active components, temperature, and flow rate on the activity and selectivity of CH4 and CO2 transformations into syngas, as well as the dynamics of CH4 and CO2 conversion on the membrane catalytic systems were studied.