In the volume fraction range (0.005,0.08), we have obtained the temporal evolution of the structure factor S(q), in extensive numerical simulations of both diffusion-limited and reaction-limited colloid aggregation in three dimensions. We report the observation of the scaling of this structure function in the diffusion-limited case, analogous to a spinodal decomposition type of scaling. By comparing S(q) with the pair correlation function between particles, we were able to identify the peak in the structure factor as arising from the correlations between particles belonging to nearest-neighbor clusters. The exponents a’ and a " that relate the position and the height of the maximum in S(q) vs time, respectively, were also obtained and shown to differ somewhat from the spinodal decomposition exponents. We also found a terminal shape for S(q) that corresponds to a close packing of the clusters after gelation. Moreover, this picture was shown to be valid in a concentration range larger than that suggested in recent experiments. Although the S(q) for reaction-limited colloid aggregation does not show a pronounced peak for the earlier times, eventually the peak stretches and becomes higher than that in the diffusion-limited case. The S(q) curves, however, do not present the scaling shown for diffusion-limited aggregation.