The present invention relates to {circle around (1)} a metal oxide or metallic Lewis acid composition comprising the metal oxide or the metallic Lewis acid carried on a cross-linked polymer compound, {circle around (2)} a metal compound composition comprising the metal compound carried on a cross-linked product of a polymer compound containing a cross-linkable condensing functional group and/or a polymer containing a polymerizable double bond formed by a condensation reaction, {circle around (3)} a method for producing a metal compound composition comprising the metal compound carried on a cross-linked polymer compound, which comprises mixing a non-cross-linked polymer compound containing a cross-linkable condensing functional group and/or a polymer compound containing a polymerizable double bond formed by a condensation reaction with a metal compound, and then cross-linking the polymer compound, {circle around (4)} a carrier for carrying a metal compound comprising a 1st polymer compound containing a cross-linkable condensing functional group and/or a 2nd polymer compound containing a polymerizable double bond formed by a condensation reaction as a non-cross-linked polymer compound and {circle around (5)} a method for improving solvent resistance, heat resistance and durability of a metal compound comprising mixing a non-cross-linked polymer compound containing a cross-linkable condensing functional group and/or a polymer compound containing a polymerizable double bond formed by a condensation reaction with a metal compound, and then cross-linking said polymer compounds.