The behavior of a chromatographic column where a single solute is fed in the presence of a suitable modifier is analyzed in the context of equilibrium theory. In particular, the pulse propagation of the solute, whose retention depends on the modifier concentration, has been analyzed as a full-fledged binary problem by the method of hodograph transformation applied to the pair of quasilinear differential equations. It has been shown that all possible operating conditions can be summarized with respect to the modifier concentration into three cases. These have been solved analytically by constructing the solution first in the hodograph plane, and then mapping it onto the physical plane using the method of characteristics. The peculiar properties of the derived hodograph plane were explained, and their impact on the pulse propagation for the three different cases has been elucidated. For the cases of intermediate adsorptivity of the modifier, the occurrence of solute peaks with infinitely high concentrations; that is, solute impulse, has been proven as well as the phenomena of double solute peaks. (D 2005 American Institute of Chemical Engineers AIChE J, 52: 565-573, 2006