A novel bankruptcy approach is proposed for resolving transboundary river conflicts in which the total water demand or claim of the riparian parties is more than the available water. Bankruptcy solution methods can allocate the available water to the conflicting parties with respect to their claims. Four commonly used bankruptcy methods in the economic literature are used here to develop new river bankruptcy solution methods for allocating water to the riparian parties of river systems. Given the non-uniform spatial and temporal distribution of water across river basins, the proposed solution methods are formulated as non-linear network flow optimization models to allocate water with respect to time sensitivity of water deliveries at different locations in a river network during the planning horizon. Once allocation optimization solutions are developed, their acceptability and stability must be evaluated. Thus, a new bankruptcy allocation stability index (BASI) is developed for evaluating the acceptability of river bankruptcy solutions. To show how the proposed river bankruptcy framework can be helpful in practice, the suggested methods are applied to a real-world transboundary river system with eight riparians under various hydrologic regimes. Stability analysis based on the proposed stability evaluation method suggests that the acceptability of allocation rules is sensitive to hydrologic conditions and demand values. This finding has an important policy implication suggesting that fixed allocation rules and treaties may not be reliable for securing cooperation over transboundary water resources as they are vulnerable to changing socioeconomic and climatic conditions as well as hydrologic non-stationarity.