The aim of this work is to take full advantage of Spectral Element (SE) and Finite Element (FE) codes by setting up a SEM/FEM co-simulation strategy for soil structure interaction problems, involving a SE code to generate and propagate elastic waves in the soil, while a FE code enables the detailed representation of the studied structure. The spatial coupling is managed by the standard coupling mortar approach, whereas the time integration is dealt with an hybrid (explicit/implicit) asynchronous (different time steps) time integrator. The SEM/FEM co-simulation strategy is set up for linear or nonlinear transient dynamics. A seismic analysis of a concrete dam is considered in order to demonstrate the versatility of the co-simulation approach, assuming a linear rheology or a nonlinear damaging behaviour of the concrete. (C) 2020 Elsevier Ltd. All rights reserved.