CO hydrogenation and the low temperature non-oxidative methane coupling to form higher hydrocarbons over Ru/SiO2 and Ru/Al2O3 prepared by incipient wetness method and Ru/Al2O3 prepared by sol/gel method (denoted by catalysts I, II and III, respectively) have been compared. Catalysts II and III possess selectivity for the formation of C5+ hydrocarbons higher than sample I and the energy of activation is 85.7 kJ/mol on the catalyst III, which is about 29-33 kJ/mol less than those measured for catalysts I and II, The striking feature of the Anderson-Schulz-Flory distribution (ASF) points to the existence of an umbilical cord mechanism and at lower temperature the reinsertion of alpha-olefins in concurrence with hydrogenolysis results in a sigmoid distribution. With increase in temperature insertion becomes more and more prevalent process and the sigmoid curve is transformed into two straight lines with different slopes, Similar behavior is valid for the "two-step reaction" in the methane coupling carried out over different ruthenium catalysts, of which sample III has the highest selectivity for C2+ hydrocarbons.