A resin composition is based on a resin selected from the group consisting of vinyl ester resins and unsaturated polyester resins, a crosslinking initiator and a crosslinking agent of general formula (I) in which i is an integer between 2 and 4, X is an i-valent group comprising at least one ring of 6 atoms selected from carbon and nitrogen and comprising at least 2 heteroatoms selected from nitrogen and oxygen, and R is an acrylate group, methacrylate group, vinyl group, alkenyl group bearing an unsaturated carbon at the chain end, or alkynyl group bearing an unsaturated carbon at the chain end.