<p>In this paper, we analyze the nonlinear dynamic response of rate-independent hysteretic rocking systems characterized by different types of complex hysteresis loop shape. Starting from the system’s equations of motion, we first transform them into a non-dimensional form thus reducing complexity and focusing on key governing parameters. Subsequently, using a continuation method based on Poincaré maps, we assess how the various hysteresis loop shapes affect frequency response, stability and bifurcation. Additionally, we explore the effects of combining different loop shapes, providing insights into their influence on system behavior. The presented results offer valuable guidance for optimizing the design of hysteretic rocking systems subjected to dynamic loads, such as earthquakes and wind.</p>