A process for the preparation of an aqueous solution or dispersion containing a cationic polymer, which comprises the steps of: polymerizing a monomer including an N-vinyl-carboxylic acid amide represented by the general formula CH2═CHNHCOR, wherein R represents a hydrogen atom or methyl group, in an aqueous medium in the presence of either or both of a polyethylene glycol and polypropylene glycol; and then modifying the resulting polymer with an acid or base. Furthermore, an aqueous composition containing a cationic polymer, which comprises (A) a modified N-vinylcarboxylic acid amide polymer, (B) either or both of a polyethylene glycol and polypropylene glycol, and (C) water is disclosed.