Conversion of methane to higher hydrocarbons by its low-temperature activation without forming undesirable carbon oxides is of great scientific and practical importance. Methane can be highly activated, yielding high rates of conversion to higher hydrocarbons and aromatics (10 to 45 percent) at low temperatures (400 degrees to 600 degrees C), by its reaction over H-galloaluminosilicate ZSM-5 type (MFI) zeolite in the presence of alkenes or higher alkanes. The methane activation results from its hydrogen-transfer reaction with alkenes.