Models for chromatographic processes consist of nonlinear convection-dominated partial differential equations (PDEs) coupled with some algebraic equations. A high resolution semi-discrete flux-limiting finite volume scheme is proposed for solving the nonlinear equilibrium dispersive model of chromatography. The suggested scheme is capable to suppress numerical oscillations and, hence, preserves the positivity of numerical solutions. Moreover, the scheme has capability to accurately capture sharp discontinuities of chromatographic fronts on coarse grids. The performance of the current scheme is validated against other flux-limiting schemes available in the literature. The case studies include single-component elution, two-component elution, and displacement chromatography on non-movable (fixed) and movable (counter-current) beds. (C) 2010 Elsevier Ltd. All rights reserved.