Sun, W. and Wang, H., 2016. Water-layer-related demultiple method using constraints in the sparse, local tau-p domain. Journal of Seismic Exploration, 25: 463-483. Water-layer-related multiple suppression remains a challenge in marine data processing. Surface-related multiple elimination (SRME) is proven to be effective in many offshore cases. As an alternative to SRME, model-based water-layer demultiple offers an effective way to predict water-layer-related multiples. In both SRME and model-based water-layer demultiple methods, the multiple contribution gather plays an important role in multiple prediction. In this paper, we propose a method to predict and subtract the water-layer-related multiples in the local tau-p domain. The sparse local tau-p transform is implemented by a weighted least-squares inversion with weights in the local tau-p domain, yielding higher resolution. Being in the local tau-p domain, the seismic data and the Green’s functions of the water-layer primary reflections can be combined such that the true downward reflection points for different water-layer-related multiple generators are automatically selected by obeying Snell’s law. In this way, the accuracy of water-layer-related multiple prediction is improved. In addition, it is proposed to replace the traditional adaptive subtraction by a filtering in the local tau-p domain, where the semblance of the predicted water-layer-related multiples can be used as constraints to identify the locations of water-layer-related multiples. Subsequently, a Butterworth-type filter can be designed to adaptively subtract the predicted water-layer-related multiples from the tau-p transformed input data. Compared with the conventional methods for adaptive subtraction via the L,-norm, our proposed method is more effective when the primaries and water-layer-related multiples are correlated. The constraints of the semblance not only provide an effective and robust way for amplitude matching, but also weaken the effects of distorted wavelets in subtraction. Our synthetic and field data examples show that the proposed flow of first predicting water-layer-related multiples and, second, separating them from the primaries by utilizing the sparse local tau-p transform enhances the water-layer-related multiple suppression results.