In an exchange-bias system, the barriers with intrinsic potential energy may be asymmetric due to unidirectional anisotropy. Based on the Stoner–Wohlfarth model, we show that the asymmetric barriers may lead to four kinds of dynamical process underlying the hysteresis-loop measurement. These kinds of dynamical processes are different in a topology-like property, which can be controlled by the orientation of the external field. In our study, a new analysis approach has been proposed to reveal the dynamical behaviors of magnetization reversal. With this approach, coercivity, exchange-bias field, and asymmetry of hysteresis loops can be quantitatively obtained.