A process for converting methane to ethane and ethylene through oxidative coupling of methane and carbon conservation has been developed. The process begins by contacting methane and an oxygen-containing stream with an oxidative coupling catalyst that is capable of reacting with carbon oxides to form a solid carbonate compound in an oxidative coupling reactor to produce an effluent containing methane, ethane, and ethylene. The solid carbonate compounds are thermally decomposed to the oxidative coupling catalyst by reaction with hot hydrogen. The oxidative coupling catalyst is then available for reuse and a stream containing hydrogen and carbon oxide by-products are produced. The stream containing hydrogen and carbon oxide by-products is contacted with a methanation catalyst in a methanation reactor to produce a stream containing methane and water. The methane is separated, dried, and recycled to the oxidative coupling reactor. Alternatively methane and an oxygen-containing stream may be contacted with an oxidative coupling catalyst in an oxidative coupling reactor to produce an effluent containing methane, ethane, ethylene and carbon oxides. The effluent is passed to an adsorption zone containing an adsorbent capable of selectively adsorbing the carbon oxides. The carbon oxides are desorbed from the adsorbent using hot hydrogen to generate a stream containing hydrogen and carbon oxides which is then contacted with a methanation catalyst in a methanation reactor to produce a stream containing methane and water. The methane is separated, dried, and recycled to the oxidative coupling reactor.