The contrast performance of current extreme adaptive optics (XAO) systems can be improved by adding a second AO correction stage featuring its own wavefront sensor (WFS), deformable mirror (DM), and real-time controller. We develop a dynamical model for such a cascade adaptive optics (CAO) system with two stages each controlled by a standard integrator and study its control properties. We study how such a configuration can improve an existing system without modifying the first stage. We analyze the CAO architecture in general and show how part of the disturbance is transferred from low to high temporal frequencies with a nefarious effect of the second stage integrator overshoot and suggest possible ways to mitigate this. We also carry out numerical simulations of the particular case of a first stage AO using a Shack–Hartmann WFS and a second stage AO with a smaller DM running at a higher framerate to reduce temporal error. In this case, we demonstrate that the second stage improves imaging contrast by one order of magnitude and shortens the decorrelation time of atmospheric turbulence speckles by even a greater factor. The results show that CAO presents a promising and relatively simple way to upgrade some existing XAO systems and achieve improved imaging contrasts fostering a large number of science case including the direct imaging of exoplanets.