An aqueous adhesive composition includes: a phenol/aldehyde resin and an unsaturated elastomer latex. The phenol/aldehyde resin is based on: an aromatic polyaldehyde bearing at least two aldehyde functional groups and including at least one aromatic nucleus; and a polyphenol including at least one aromatic nucleus. If there is just one aromatic nucleus, the nucleus bears two or three hydroxyl functional groups in a meta position with respect to each other or with respect to one another, with a remainder of the nucleus being unsubstituted. If there are plural aromatic nuclei, at least two of the nuclei each bear two or three hydroxyl functional groups in the meta position with respect to each other or with respect to one another, with two positions ortho to at least one of these hydroxyl functional groups being unsubstituted. The adhesive composition is useable to adhere a textile material to a crosslinkable rubber composition.