The local equilibrium theory of chromatography is applied to binary systems subject to the generalized Langmuir isotherm. This newly introduced adsorption isotherm allows describing a variety of competitive and synergistic adsorption behaviors, by letting each of the two components be Langmuir-like or anti-Langmuir-like. It is shown that all four possible types of isotherms (one of which is the classical competitive Langmuir isotherm) share the key property that characteristics in the composition plane are straight lines-hence, the application of the method of characteristics leads to explicit expressions-and the solution of Riemann problems, e. g., elution of a saturated column or adsorption on an initially clean column, boils down to the use of simple algebraic relationships. Similarities and differences among the four different cases are presented, analyzed, and discussed, including their physical legitimacy and thermodynamic consistency, particularly for the case where the first eluting component is anti-Langmuir-like and the second eluting component is Langmuir-like. The significance of the theoretical findings on chromatographic column dynamics is also discussed. Finally, the results are extended to a moving bed adsorber, as a preliminary step toward the use of the theory for the design of multicolumn chromatographic separations, e. g., simulated moving bed processes.