Phase separation in binary and ternary fluids is studied using a two-dimensional lattice gas automata. The lengths given by the the first zero crossing point of the correlation function and the total interface length is shown to exhibit power law dependence on time. In binary mixtures, our data clearly indicate the existence of a regime having more than one length scale, where the coarsening process proceeds through the rupture and reassociation of domains. In ternary fluids; in the case of symmetric mixtures there exists a regime with a single length scale having dynamic exponent [Formula presented] while in asymmetric mixtures our data establish the break down of scale invariance. © 2003 The American Physical Society.