A new dynamical energy system model representation is given for threshold networks. Inspired by the relation between stability and dissipativeness of dynamical systems, the convergence property of threshold networks is investigated. Using the energy function inherent within the given model a condition, namely the dissipativeness of the dynamical system, necessary and sufficient condition for the convergence of the threshold network to a fixed point, is given. Also, an easy to check inequality is stated to test the convergence of the threshold network. Copyright (C) 2000 John Wiley & Sons, Ltd.