  We present a unified group-theoretical framework for superparticle theories.
This explains the origin of the ``twistor-like'' variables that have been used
in trading the superparticle's $\kappa$-symmetry for worldline supersymmetry.
We show that these twistor-like variables naturally parametrise the coset space
${\cal G}/{\cal H}$, where $\cal G$ is the Lorentz group $SO^\uparrow(1,d-1)$
and $\cal H$ is its maximal subgroup. This space is a compact manifold, the
sphere $S^{d-2}$. Our group-theoretical construction gives the proper
covariantisation of a fixed light-cone frame and clarifies the relation between
target-space and worldline supersymmetries.
