Spinodal decomposition of colloids in the initial and intermediate stages is described on the. basis of the Smoluchowski equation. Hydrodynamic interaction is treated in an approximate way. In the intermediate stage, where a dominant length scale exists, the static structure factor is found to exhibit universal scaling behavior. The corresponding dynamic scaling function is derived from the nonlinear equation of motion for the static structure factor. This scaling function is a much more sharply peaked function of the wave vector than the well-known empirical Furukawa scaling function, which applies to the transition stage where sharp interfaces contribute considerably, giving rise to a Porod tail at larger wave vectors. The wave vector where the static structure factor exhibits a maximum is found to vary with time-in the intermediate stage-like similar to t(-alpha), where the exponent alpha varies between 0.2 and 1.1, depending on the relative importance of hydrodynamic interaction. Experiments on a microemulsion and binary polymer melt confirm the predicted scaling behavior.