An aqueous adhesive composition comprises a phenol/aldehyde resin and less than 16% by weight of unsaturated diene elastomer latex. The phenol/aldehyde resin is based on an aromatic polyaldehyde bearing at least two aldehyde functional groups and comprising at least one aromatic nucleus, and on a polyphenol comprising one or more aromatic nuclei. If just one aromatic nucleus is present, the latter bears two or three hydroxyl functional groups in the meta position with respect to one another and the remainder of the aromatic nucleus is unsubstituted. If several aromatic nuclei are present, at least two of them each bear two or three hydroxyl functional groups in the meta position with respect to one another, it being understood that the two positions ortho to at least one of these hydroxyl functional groups are unsubstituted.