Abstract: A mathematical simulation of the dispersion of a sample injected in a viscosity-controlled (Poiseuille flow) stream has been made to determine the behavior of the sample from injection time until the sample distribution has become substantially gaussian. The results show that for velocities much greater than the chromatographic optimu, and for flow of the order one to ten theoretical plate heights, an unusually unsymmetrical distribution develops. It gives rise to doubly peaked chromatograms, in agreement with curves actually observed in corresponding experiments.