The two-twistor formulation of particle mechanics in D-dimensional anti-de
Sitter space for D=4,5,7, which linearises invariance under the AdS isometry
group Sp(4;K) for K=R,C,H, is generalized to the massless N-extended "spinning
particle". The twistor variables are gauge invariant with respect to the
initial N local worldline supersymmetries; this simplifies aspects of the
quantum theory such as implications of global gauge anomalies. We also give
details of the two-supertwistor form of the superparticle, in particular the
massive superparticle on AdS_5.