Subclass of bony fish comprising both fossil and living lobe-finned or tassel-finned fish, including the Coelacanthiformes and Rhipidistia. The former are well known from Palaeozoic and Mesozoic rocks, but were thought to have become extinct by the end of the Cretaceous until living specimens were netted last century in the Indian Ocean. The Rhipidistia did become extinct, although not before they gave rise, in the Devonian, to the amphibians. The Crossopterygii are characterized by the fact that all fins (except the tail-fin) are based on movable stalks or lobes. The tail fin is either heterocercal or diphycercal.