  In this paper we consider the conformal dynamics for a system of $N$
interacting relativistic massless particles. A detailed study is done for the
case of two-particles, with a particular attention to the symmetries of the
problem. In fact, we show that this analysis could be extended to the case of
higher spin symmetries. Always in the two particle case a formulation in terms
of bilocal fields is proposed. For a system of $N$ particles we consider two
possible scenarios: i) action invariant under any permutation of the $N$
particles. This case corresponds to completely democratic interactions with
each particle interacting with all the others. The action depends on $N-1$
dimensionless coupling constants. ii) By putting the particles along a
one-dimensional lattice (open or closed) with nearest neighbor interactions,
one obtains a model with only two-body interactions depending on a single
dimensionless coupling. This model can be easily extended to the continuum
case, obtaining a conformal string-like (closed or open) system.
