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We investigate Jordan isomorphisms of triangular rings and give a sufficient condition under which they are necessarily isomorphisms or antiisomorphisms. As corollaries we obtain generalizations of two recent results: the one concerning Jordan isomorphisms of triangular matrix algebras by Beidar, Brešar and Chebotar, and the one concerning Jordan isomorphisms of nest algebras by Lu.doi:10.1090/s0002-9939-05-07989-x fatcat:pbq2icfilbbtthv3lir6gccyiy