Oxygen isotope fractionations involving carbonates and sulfates have been controversial for a long time. There are important unresolved conflicts among the results of theoretical calculations, experimental measurements and empirical estimates. In this paper, the increment method is adapted to systematically evaluate oxygen isotope fractionations in the carbonates and sulfates. The following sequence of 18-enrichment in carbonate minerals is obtained: siderite > ankerite > magnesite ≥ dolomite > calcite > aragonite > strontianite > cerussite ≥ witherite. The sequence of 18O-enrichment in sulfate minerals is predicted as follows: anhydrite > celestite > barite > anglesite. The internally consistent fractionation factors for the systems carbonate-water and sulfate-water are acquired for a temperature range of 0 to 1200°C, which are in fair agreement with existing experimental and/or empirical data. The present calculations suggest that dolomite should behave isotopically like calcite; equilibrium fractionation between dolomite and calcite is only 0.56‰ at 25°C. Aragonite is predicted to be significantly depleted in 18O relative to calcite; equilibrium fractionation between calcite and aragonite is 4.47‰ at 25°C. It is possible that polymorphic transition from aragonite to calcite could proceed through an essentially intact oxygen structure without isotopic resetting. As a result, the temperature dependence of oxygen isotope partitioning in aragonite could be conveyed to calcite. Oxygen isotope inheritance in calcite formation by the polymorphic transition may be of critical importance in attempts to resolve dilemma involving fractionations in aragonite-calcite-dolomite-water systems.