This paper presents a theoretical treatment of the evolution of the carbon isotopes C13 and C14 in natural waters and in precipitates which derive from such waters. The effects of an arbitrary number of sources (such as dissolution of carbonate minerals and oxidation of organic material) and sinks (such as mineral precipitation, CO2 degassing and production of methane), and of equilibrium fractionation between solid, gas and aqueous phases are considered. The results are expressed as equations relating changes in isotopic composition to changes in conventional carbonate chemistry. One implication of the equations is that the isotopic composition of an aqueous phase may approach a limiting value whenever there are simultaneous inputs and outputs of carbonate. In order to unambiguously interpret isotopic data from carbonate precipitates and identify reactants and products in reacting natural waters, it is essential that isotopic changes are determined chiefly by reactant and product stoichiometry, independent of reaction path. We demonstrate that this is so by means of quantitative examples. The evolution equations are applied to: 1. (1) carbon-14 dating of groundwaters; 2. (2) interpretation of the isotopic composition of carbonate precipitates, carbonate cements and diagenetically altered carbonates; and 3. (3) the identification of chemical reaction stoichiometry. These applications are illustrated by examples which show the variation of ??C13 in solutions and in precipitates formed under a variety of conditions involving incongruent dissolution, CO2 degassing, methane production and mineral precipitation. ?? 1978.