Abstarct: In this thesis in the first in chapter , biological and artificial neural networks are explained. Then in the second chapter, stability of neural networks are given. By considering the delayed cell neraul network in chapter 3, we show that the equilibrium point is unique. Then by presenting a suitable Lyapunov–Krasovskii function and using the linear matrix inequality we prove that the system is asymptotically stable. In chapter 4, by considering a delayed daynamic system of the Cohen–Grossberg delay network and presenting a suitable Lyapunov–Krasovskii function, and using the linear matrix inequality, as well as the Halanay inequality technique, we prove that the system is asymptotically stable and exponentially stable.