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The movement of a particular component along an HPLC column is studied on the ba-sis of equilibrium equations. Numerical simulation of multi--step gradient elution HPLC isperformed by means o? a personal computer program. The location x, as a fraction of thecolumn length, for a given time t o? each compound is calculated, the velocity and corre-sponding acceleration are given as well. Diagrams for x,dx/dt and d~2x/dt~2 versus t display themovement process of the different components along the HPLC column during gradient elu-tion. The prediction of the retention time and peak width, and the optimization for the multi-step gradient elution HPLC are all based on such simulation and the molecular structure ofthe. components is separated as well.