The work presented in this publication can be categorized among domain decomposition methods of the dual Schur type applied to structural dynamics. This approach leads to lower CPU times and better control of the accuracy of the time discretization and allows to take into account multi-time-scale effects which arise in transient structural dynamics. In order to consider incompatible time scales, one has to enforce continuity at the interfaces between the subdomains. Here, we propose a general formalism which enables the coupling of subdomains with their own numerical time integration scheme. The proposed method enables one to take into account possible nonlinearities which may present different time scale between the subdomains in a general manner for a wide range of time numerical scheme. This method also offers an important improvement for industrial software with easy implementation. Linear and nonlinear numerical examples are proposed in order to show the efficiency and the robustness of the method.