Method of producing multicomponent copolymer

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Provided is a method of producing a multicomponent copolymer, in which ethylene, a non-conjugated olefin compound having 3 to 10 carbon atoms, and a conjugated diene compound are copolymerized to produce a multicomponent copolymer. The method of producing a multicomponent copolymer is a method in which ethylene, a non-conjugated olefin compound having 3 to 10 carbon atoms, and a conjugated diene compound are copolymerized to produce a multicomponent copolymer, including a step of copolymerizing the ethylene, the non-conjugated olefin compound, and the conjugated diene compound, in the presence of a polymerization catalyst composition containing a rare earth element compound (component (A)) represented by predetermined formula.