The existence of concentration shocks due to nonlinearity of the adsorption isotherm is the feature of simultaneous adsorption and reaction processes in a fixed bed. A new approach to the shock is suggested in this paper. The shocks are regarded as moving boundaries which cut the spatial domain into separate "smooth" subregions

and the consistency equations on the shocks are taken as boundary conditions or connection ones that link the adjacent subregions. Then

a moving coordinate following the movement of the shocks is introduced and the shock discontinuities are transformed into fixed boundaries in the coordinate. Finally

simple trial functions are used to approximate concentration profiles in the smooth region

and the integral form of the governing equations provide a close set of first order ordinary differential equations. By the method

the problem of migration of two components with Langmuirian adsorption and reversible reactions is greatly simplified to that of four ODEs. A complete solution for the problem is obtained

and the characteristics of the shock movement under various conditions are discussed. It is found that when the weakly adsorptive reactant A is initially dominant

a maximum of distance between the two shocks exists there

and for irreversible reactions

the A - rich region does not disapear even when A is depleted

it becomes a constant thin layer between two shocks in the end of the movement.