  We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7
from twistors describing massless (super-)particles on AdS spaces. A massless
twistor transform is derived in a geometric way from classical kinematics.
Relaxing the spin-shell constraints on twistor space gives an infinite tower of
massless states of a ``higher spin particle'', generalising previous work of
Bandos et al. This can generically be done in a number of ways, each defining
the states of a distinct higher spin theory, and the method provides a
systematic way of finding these. We reproduce known results in D=4, minimal
supersymmetric 5- and 7-dimensional models, as well as supersymmetrisations of
Vasiliev's Sp-models as special cases. In the latter models a dimensional
enhancement takes place, meaning that the theory lives on a space of higher
dimension than the original AdS space, and becomes a theory of doubletons. This
talk was presented at the XIXth Max Born Symposium ``Fundamental Interactions
and Twistor-Like Methods'', September 2004, in Wroclaw, Poland.
