In this paper we consider 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) the action is 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 stringlike (closed or open) system.