Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convec- tion and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equa- tions based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of con- temporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics. Under the framework of non-equilibrium thermodynamic separation theory (NTST), the Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convection and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equa- tions based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of con- temporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics.