Carrier-free strontium and cesium isotopes were used to study the heterogeneous exchange of the systems strontium/strontium carbonate and cesium/cesium tetraphenylborate. The elements under consideration are among the long-lived isotopes most desired to be removed from waste solutions and consequently the use of heterogeneous exchange as an applied phenomenon for selective fixation is possible. The results obtained show that the above two systems are unstable ones (i. e., undergoing either formation or dissolution of the precipitated solid phase). New modified equations were proposed for quantitative calculation of the fraction of exchange, using only radiometric data and avoiding the use of microanalytical data. The equations are useful for all unstable systems, especially if no precise microquentitative method of analysis is known for the element under consideration. Recrystallization and self-diffusion were proposed to explain the two parts characterizing the exchange curves.