An axial dispersion model for the operation of a fixed-bed adsorber with a linear adsorption isotherm was formulated and solved analytically using the separation of variables method. The asymptotic solution for a large Peclet number and/or a small operation time was also obtained using two limiting cases. The results can be used to correlate or to predict both the mass-transfer zones and the breakthrough curves of a fixed-bed adsorber. Influence of both the Peclet number and the retardation coefficient on the operation of a fired-bed adsorber was also studied As an example, the axial dispersion model was applied to the experimental data of the removal of phenol from the solution in the activated carbon and the Amberlite resin XAD-4 fixed-bed adsorbers.