  This paper is concerned with theories describing spinning particles that are
formulated in terms of actions possessing either local world-line supersymmetry
or local fermionic {\it kappa} invariance. These classical actions are obtained
by adding a finite number of spinor or vector coordinates to the usual
space-time coordinates. Generalizing to superspace leads to corresponding types
of \lq spinning superparticle' theories in which the wave-functions are
superfields in some (generally reducible) representation of the Lorentz group.
A class of these spinning superparticle actions possesses the same spectrum as
ten-dimensional supersymmetric Yang--Mills theory, which it is shown can be
formulated in terms of either vector or spinor superfields satisfying
supercovariant constraints. The models under consideration include some that
were known previously and some new ones.
