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The simulation in real time of heterogeneous systems has to guarantee that the time integration of the equations of motion is always successfully completed within an a priori fixed sampling time interval. Therefore, numerical and/or physical substructures as well as numerical solution methods have to be adapted to the needs of real-time simulations. Monolithic stable numerical methods are implicit and cannot be easily used in real-time applications because of their iterative strategies necessary to solve the nonlinear corrector equations. As an alternative, in the present paper, we consider linearly implicit Rosenbrock-based L-stable real-time (LSRT) compatible algorithms with both two-stage and three-stage. Moreover, other linearly implicit structural integrators used nowadays to perform coupled simulations in real time are introduced too. Successively, typical properties of monolithic algorithms are shown when large time steps are employed. The loss of stability and the reduction of accuracy of these algorithms, when applied to coupled systems caused by kinematically closed loops, are analyzed in-depth through a split-inertia substructured system. In this respect, the benefits of the L-stability property are shown. Finally, the performance of the algorithms under investigation appears in a number of more realistic tests considering both nonstiff and stiff substructures. [ABSTRACT FROM AUTHOR]