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• Dynamic substructuring is extended to time-variant interfaces due to a sliding contact. • Time dependent compatibility and equilibrium conditions are considered • The problem is solved in the time domain using primal and dual assembly. • Time Dependent Frequency Response Functions (TD-FRFs) are defined. • A lumped parameter model and to a discretized continuous system are studied. The study of complex systems composed by substructures connected together by frictional interfaces can benefit of the framework developed for dynamic substructuring. These systems are generally composed by time-invariant substructures in relative motion, implying time variant contact interfaces. Although the classical formulations of dynamic substructuring deal with time-invariant systems, they can be extended to include time-invariant component subsystems subjected to time-variant coupling conditions. The problem can be tackled in time domain using both primal and dual assembly, and in time-frequency domain using dual assembly to obtain the Time Dependent Frequency Response Functions (TD-FRFs). The equilibrium and the compatibility conditions are time-dependent and have to be defined under the assumption that the relative sliding motion at the contact interfaces is known a priori, at least approximately. The proposed method is applied to a lumped parameter model in order to evaluate its feasibility, and to a finite element model to verify its effectiveness. [ABSTRACT FROM AUTHOR]