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Abstract. A tsunami generated by large-volume landslide can propagate across the ocean and flood communities around the basin. The evolution of landslide-generated tsunamis is affected by the effects of frequency dispersion and involves processes of different temporal and spacial scales. In this paper, we develop a numerical approach employing the weakly nonlinear and fully nonlinear Boussinesq-type theories and nested computational grids. The propagation in a large domain is simulated with the weakly nonlinear model in a geographical reference frame. The nearshore wave evolution and runup are computed with the fully nonlinear model. Nested grids are employed to zoom simulations from larger to smaller domains at successively increasing resolutions. The models and the nesting scheme are validated for theoretical analysis, laboratory experiments and a historical tsunami event. By applying this approach, we also investigate the potential tsunami impact on the US east coast due to the possible landslide on La Palma Island. The scenario employed in this study represents an event of extremely low probability.