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.

Version accepted for publication in Phys. Rev. D