This work is concerned with the bifurcational analysis of nonlinear dissipative systems affected by time delay. This issue typically arises when testing highly nonlinear energy dissipation devices, commonly used in vibration control of civil structures, and carried out experimentally via a hybrid technique known as Real-Time Dynamic Substructuring (RTDS) simulation. Unfortunately, the RTDS simulation is affected by time delay in the control feedback loop due to the actuator response, sensor reading and numerical processing. In essence, this paper focuses on studying the nonlinear dynamics induced by the interaction of a dynamical system with the nonlinear damper affected by the presence of time delay. Given the complexity of the system, numerical analysis is carried out in the context of bifurcational behavior, and bifurcation diagrams are computed using a continuation method. The bifurcational analysis presented here, provides a characterization of delay-induced nonlinear phenomena created by the interaction of the dynamical system with a delayed nonlinear response of the dissipation device. Nonlinear dynamics are also identified and characterized for different damper types when varying the damper model parameters, leading to the identification of system conditions at which the testing arrangement and test specimens can exhibit undesired dynamics.