During development of a dynamical model to simulate the central T-cell subsystem of the human immune system, its extraordinary stability lead to the assumption that it might be deduced solely from stability considerations. We demonstrate that linear stability conditions together with additional general requirements indeed define a low number (of the order of 10) of dynamical systems from about 1.E10 possibilities for systems with up to four components. At least two of the most simple ten linearly stable systems play central roles in biology, indicating that stable dynamical subsystems resulting from evolutionary processes might be understood on a mathematical basis. We expect that our ten dynamical subsystems are generic and will be found as basic building blocks in biological, social or technical systems.