The stickiness effect of invariant tori in the phase space is widely studied, and extended to the slow-down of orbital diffusion due to some other invariant sets, such as Cantori, island-chains and hyperbolic periodic orbits.We report on two models in which hyperbolic periodic orbits show the stickiness effect. We discuss the generalized stickiness effects caused by different invariant sets. We believe that the main cause of the generalized stickiness effects is the hyperbolic structures in the phase space of the dynamical systems.