Conversion of methane in high yields to C4+ nonaromatic hydrocarbons was demonstrated in a recycle system. The principal components of the recycle system included an oxidative coupling reactor with a Mn/Na2WO4/SiO2 catalyst at 800 degrees C for conversion of methane to ethylene, and a reactor with an H-ZSM-5 zeolite at 275 degrees C for subsequent conversion of ethylene to higher hydrocarbons. Total yields of C4+ products were in the range of 60-80%, and yields of C4+ nonaromatic hydrocarbons were in the range of 50-60%.