Enzymes of the isomerase class that catalyze the oxidation of one part of a molecule with a corresponding reduction of another part of the same molecule. They include enzymes converting aldoses to ketoses (ALDOSE-KETOSE ISOMERASES), enzymes shifting a carbon-carbon double bond (CARBON-CARBON DOUBLE BOND ISOMERASES), and enzymes transposing S-S bonds (SULFUR-SULFUR BOND ISOMERASES). (From Enzyme Nomenclature, 1992) EC 5.3.