Rubber mounts are elements of extreme importance in automotive suspension, and accurate modeling is crucial for comfort design. While mount characterization is typically done using cycles, actual performance is often associated with transients. The paper thus focuses on the impact of power dissipation on suspension models during transients. For scalar or 0D hysteretic models that respect Madelung rules and Masing’s law, a method is introduced to compute instant dissipation even for models where it is not explicitly available. It is shown that stiffness and dissipation depend only on the last turning point and this dependence should be the core aspect for identifying and modeling hysteretic dissipation. The second section introduces two different 0D models having the same full cycle dissipation and force amplitude, thus the same storage and loss moduli in a first harmonic approximation of the mount behavior, though having different instantaneous dissipation. The case of a transient starting torque soliciting a suspended powertrain is finally considered. The different suspension models are shown to have different instant dissipation which might deeply modify the conclusions drawn from the dynamic simulation.