We consider the stability and design of the general non-symmetric Hopfield neural network. The stability of equilibria is analysed through the linearized system and a stability criterion is derived. Bounds of the equilibria are obtained and can be used to start off iterative processes in the computation of the equilibria. The design problem is shown to be equivalent to an inverse eigenvalue problem and is analysed using pole assignment techniques in control theory. The novel and efficient algorithm for the design of Hopfield neural networks with a given equilibrium is then presented. Two illustrative examples are given.