Two numerical procedures for the solution of a non-linear multicomponent chromatography model have been developed. The applied model includes axial dispersion in the external fluid phase, interphase mass transfer resistances and variation of fluid velocity. First solution technique is based on the method of lines, in which the space variables are discretized using the orthogonal collocation method on moving finite elements, coupled with an integration method for stiff ordinary differential equations. An efficient procedure for updating during the integration of the position of the finite element boundaries, in order to follow the movement of peaks, is proposed. Second solution technique is a very fast finite difference method. The influence of fluid velocity variation on retention time for liquid chromatography (LC) and high performance liquid chromatography (HPLC) is presented.