  In analogy to Wong's equations describing the motion of a charged
relativistic point particle in the presence of an external Yang-Mills field, we
discuss the motion of such a particle in non-commutative space subject to an
external $U_\star(1)$ gauge field. We conclude that the latter equations are
only consistent in the case of a constant field strength. This formulation,
which is based on an action written in Moyal space, provides a coarser level of
description than full QED on non-commutative space. The results are compared
with those obtained from the different Hamiltonian approaches. Furthermore, a
continuum version for Wong's equations and for the motion of a particle in
non-commutative space is derived.
