Polyalkenyl ether is produced by polymerizing alkenyl ether represented by the following general formula (I): CHR1═CH(OR2)  (I) wherein R1 represents a hydrogen atom or a methyl group, R2 represents a monovalent organic group, and R2 contains a silicon atom or at least one atom selected from the group consisting of elements from group 15 to group 17, in the presence of a halide of an element other than Al, or an organometallic compound of an element other than Al, and a nonionic oxygen-containing or nonionic nitrogen-containing organic compound.