Composite (P1, P2) comprising: - at least one reinforcing element, - an adhesive layer made from an adhesive composition and coating the reinforcing element, - an elastomeric body made from an elastomeric matrix comprising at least one elastomer selected from the group consisting of an ethylene/alpha-olefin type elastomer, a polychloroprene elastomer and the mixtures of these elastomers and embedded in which elastomeric body is the reinforcing element coated with the adhesive layer, the composite (P1, P2) being characterized in that the adhesive composition comprises at least one resin based: • on at least one aromatic polyphenol comprising at least one aromatic ring bearing at least two hydroxyl functions in the meta position relative to one another, the two positions ortho to at least one of the hydroxyl functions being unsubstituted, and/or • on at least one aromatic monophenol comprising at least one six-membered aromatic ring bearing a single hydroxyl function, ∘ the two positions ortho to the hydroxyl function being unsubstituted, or ∘ at least one position ortho to and the position para to the hydroxyl function being unsubstituted, and • on at least one aromatic compound comprising at least one aromatic ring bearing at least two functions, one of these functions being a hydroxymethyl function and the other being an aldehyde function or a hydroxymethyl function. - at least one reinforcing element, - an adhesive layer made from an adhesive composition and coating the reinforcing element, - an elastomeric body made from an elastomeric matrix comprising at least one elastomer selected from the group consisting of an ethylene/alpha-olefin type elastomer, a polychloroprene elastomer and the mixtures of these elastomers and embedded in which elastomeric body is the reinforcing element coated with the adhesive layer, the composite (P1, P2) being characterized in that the adhesive composition comprises at least one resin based: • on at least one aromatic polyphenol comprising at least one aromatic ring bearing at least two hydroxyl functions in the meta position relative to one another, the two positions ortho to at least one of the hydroxyl functions being unsubstituted, and/or • on at least one aromatic monophenol comprising at least one six-membered aromatic ring bearing a single hydroxyl function, ∘ the two positions ortho to the hydroxyl function being unsubstituted, or ∘ at least one position ortho to and the position para to the hydroxyl function being unsubstituted, and • on at least one aromatic compound comprising at least one aromatic ring bearing at least two functions, one of these functions being a hydroxymethyl function and the other being an aldehyde function or a hydroxymethyl function. • on at least one aromatic polyphenol comprising at least one aromatic ring bearing at least two hydroxyl functions in the meta position relative to one another, the two positions ortho to at least one of the hydroxyl functions being unsubstituted, and/or • on at least one aromatic monophenol comprising at least one six-membered aromatic ring bearing a single hydroxyl function, ∘ the two positions ortho to the hydroxyl function being unsubstituted, or ∘ at least one position ortho to and the position para to the hydroxyl function being unsubstituted, and ∘ the two positions ortho to the hydroxyl function being unsubstituted, or ∘ at least one position ortho to and the position para to the hydroxyl function being unsubstituted, and • on at least one aromatic compound comprising at least one aromatic ring bearing at least two functions, one of these functions being a hydroxymethyl function and the other being an aldehyde function or a hydroxymethyl function.