Abstract. We show that weak convergence of point measures and (2 + ǫ)-moment conditions imply hydrodynamic equations at the limit of infinitely many interacting molecules.The conditions are satisfied whenever the solutions of the classical equations for N interacting molecules obey uniform in N bounds. As an example, we show that this holds when the initial conditions are bounded and that the molecule interaction, a certain N -rescaling of potentials that include all r −p for 1 < p, is weak enough at the initial time. In this case the hydrodynamic equations coincide with the macroscopic equations of Maxwell.