An aqueous dispersion that comprises: (A) a polyolefin terpolymer resin obtained from (a) an unsaturated carboxylic acid or anhydride thereof, (b) an ethylenic hycrocarbon, and (c) a specific compound, the proportion of (a) being 0.01 to 5 wt %, excluding 5 wt %, and the ratio of (b) to (c) being from 55/45 to 99/1 (wt %); (B) a basic compound; and (C) an aqueous medium, that the polyolefin terpolymer resin (A) dispersed in the aqueous medium has a number-average particle diameter of 1 &mgr;m or smaller, and that the dispersion contains substantially no nonvolatile water-compatibilizing agent. Also provided are a coated film obtained by applying this aqueous dispersion to a thermoplastic resin and a coated metal material obtained by applying this aqueous dispersion to a metal material.