The invention provides a crosslinking agent comprising a compound having at least two noncyclic acid anhydride groups and represented by the following formula ##STR1## wherein R is a monovalent hydrocarbon group having 2 to 50 carbon atoms, R' is a bivalent hydrocarbon group having 2 to 50 carbon atoms, the hydrocarbon groups R and R' containing or not containing an ether linkage, urethane linkage or ester linkage, and n is an integer of 1 to 500.The invention also provides a curable composition including (A) at least one resin selected from the group consisting of (i) a resin having at least one epoxy group and at least one hydroxyl group in the molecule, (ii) a resin mixture of a resin having at least two epoxy groups in the molecule and a resin having at least two hydroxyl groups in the molecule, and (iii) a resin having at least two epoxy groups in the molecule, and (B) the above-mentioned crosslinking agent.