NOVELTY - Hydrocarbon is methanated by contacting mixed gas consisting of aliphatic and/or aromatic hydrocarbon and hydrogen with catalyst at increased temperature, hydrocracking aliphatic and/or aromatic hydrocarbon, and converting into methane. Catalyst contains (1) 18-70 at.% zirconium (Zr) and (2) 1-20 at.% group of elements consisting of yttrium (Y), lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), samarium (Sm), gadolinium (Gd), dysprosium (Dy), calcium (Ca), and/or group consisting of magnesium (Mg) which are tetragonal-system zirconia structure stabilization elements.    USE - Methanation of hydrocarbon used as starting material in synthetic chemistry and as gaseous fuel.    ADVANTAGE - Failure in assigning to use with undesirable natural gas containing components other than methane is removed, yield of natural gas is improved, process of isolating hydrocarbon containing greater than or equal to 2 carbons becomes unnecessary, emission of useless carbon dioxide is avoided, repetition of reaction numerous times by high pressure is prevented, simple apparatus operated by normal pressure is used without requiring complicated installation of raw material circulation, and manufacture of catalyst is easy.    DETAILED DESCRIPTION - Hydrocarbon is methanated by contacting mixed gas consisting of aliphatic and/or aromatic hydrocarbon and hydrogen with catalyst at increased temperature, hydrocracking aliphatic and/or aromatic hydrocarbon, and converting into methane. Catalyst contains (1) 18-70 at.% zirconium (Zr), (2) 1-20 at.% group of elements consisting of yttrium (Y), lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), samarium (Sm), gadolinium (Gd), dysprosium (Dy), calcium (Ca), and/or group consisting of magnesium (Mg) which are tetragonal-system zirconia structure stabilization elements, and (3) 25-80 at.% iron group element in which nickel (Ni) occupies greater than or equal to 0.6 by an atomic ratio. The iron group element of metal state uses catalyst supported as active-type which bears catalyst activity for a carrier consisting of multiple oxide of tetragonal-system zirconia structure which contains iron group elements into crystal structure and is stabilized with stabilization element. INDEPENDENT CLAIMS are included for:    (1) processing of natural gas which involves contacting mixed gas consisting of natural gas with greater than or equal to 2 carbon-containing hydrocarbon with methane, contacting hydrogen with catalyst at increased temperature, hydrocracking hydrocarbon contained in natural gas, and converting into methane; and    (2) manufacture of methanation reaction catalyst which involves mixing aqueous solution of salt of component (1) with hydro-sol of zirconia (Zr), concentrating-drying mixture, heating, and reduction-processing.