The present invention relates to a tyre comprising a rubber composition with a base of at least one ethylenic elastomer comprising epoxide functions as the majority elastomer, at least one reinforcing filler, and a cross-linking system comprising a polycarboxylic acid with general formula (I) in which A represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atoms, optionally substituted and optionally interrupted by one or more heteroatoms, and an imidazole with general formula (II) in which R1 represents a hydrocarbon group or a hydrogen atom, R2 represents a hydrocarbon group, R3 and R4 represent, independently of each other, a hydrogen atom or a hydrocarbon group, or R3 and R4 form a cycle together with the carbon atoms of the imidazole cycle to which they bond.