The demand for the new development of specific separation techniques for the treatment of drinking water leads to re-examining the use of cyclic operations in ion exchange processes. Establishing stable limit fronts inside the column is the required condition to allow the use of two-way chromatography methods and insure the process efficiency. This paper presents numerical simulations and experimental validation at a laboratory pilot scale showing the development of a set of stationary composition profiles during a cyclic operation of a chromatographic ion-exchange cyclic process. It has been shown numerically that stable cycles are obtained in the case where the cut points are chosen following a criterion based on the breakthrough volumes. The properties displayed by means of numerical simulations were experimentally validated. Reconstituted waters were treated by the cyclic process in order to selectively eliminate fluoride ion. The process uses two anion-exchange columns pre-equilibrated with the hydrogen carbonate anion in excess in the feed solution. After some cycles, steady concentrations of the major species (chloride and sulphate ions) are measured: a stable limit cycle is reached and the condition to (i) eliminate fluoride anion, (ii) restore the matrix of the other anions is fulfilled.