  The classical far field concept of wave velocities has its merits while
exibiting intrinsic difficulties. A general local approach for the definition
of velocities and especially phase velocities for waves avoiding these
difficulties is proposed. It includes the classical definitions as particular
cases and can be applied to waves of an arbitrary structure, and to arbitrary
propagation media as well. Applications of the formalism are elucidated and
some basic properties of the local concept defined here are discussed.
