  A 'Liouville structure' is a structure isomorphic to a cotangent vector
fibration. A Liouville structure is an essential ingredient of every
variational formulation of a physical theory. For reasons of interpretation the
Liouville structure can not be replaced by the corresponding cotangent
fibration. We give a precise definition of Liouville structures, study their
properties, and give examples used in variational formulations of mechanics.
