We will consider the conformal dynamics for a system of $N$ interacting relativistic massless particles. A detailed study for the case of two-particles with a particular attention to the symmetries of the problem will be presented In the case of $N$ particles we will consider two possible scenarios: i) action invariant under any permutation of the $N$ particles. ii) By putting the particles along a one-dimensional lattice with nearest neighbor interactions, one obtains a model with only two-body interactions. This model can be easily extended to the continuum case, obtaining a conformal string-like system. The extension to the supersymmetric massless particles will be outlined.