Oxygen-scavenging polyester compositions are disclosed that comprise one or more polyesters having incorporated therein residues of 3-hexenedioic acid and terephthalic acid. The compositions may further comprise residues of one or more aliphatic dicarboxylic acids such as adipic acid. One or more of the polyesters of the compositions may comprise significant amounts of repeating units of polyethylene terephthalate as homopolymers or copolymers, making them suitable for us in packaging compositions having oxygen-scavenging properties.