Disclosed is a process for producing C2+ hydrocarbons, and systems for implementing the process, that includes providing a reactant feed that includes methane and an oxygen containing gas to a first reaction zone, wherein the temperature of the reactant feed is less than 700° C. contacting the reactant feed with a first catalyst capable of catalyzing an oxidative coupling of methane reaction (OCM) to produce a first product stream that includes C2+ hydrocarbons and heat, and contacting the first product stream with a second catalyst capable of catalyzing an OCM reaction to produce a second product stream that includes C2+ hydrocarbons, wherein the produced heat is at least partially used to heat the first product stream prior to or during contact with the second catalyst, wherein the amount of C2+ hydrocarbons in the second product stream is greater than the amount of C2+ hydrocarbons in the first product stream.