The nonoxidative conversion of methane to aromatic hydrocarbons in the presence of a high-silica ZSM-5 zeolite modified with molybdenum and rhenium nanopowders has been studied. Data on the acid characteristics of the catalysts have been derived by temperature-programmed desorption of ammonia. The microstructure and composition of the Re/ZSM-5 and Re-Mo/ZSM-5 catalyst systems have been studied by transmission electron microscopy. It has been shown that modification of a Mo-containing zeolite with rhenium leads to an increase in the activity and stability of the catalyst in the methane dehydroaromatization reaction.