MPEJ Volume 3, No.1, 36pp Received: September 24, 1996, Accepted: March 18, 1997 V.A. Malyshev, F.M. Spieksma Dynamics in Binary Neural Networks with a Finite Number of Patterns. Part 1. General Picture of the Asynchronous Zero Temperature Dynamics. ABSTRACT: We rigorously define and study the limiting dynamics for Pastur-Figotin-Hopfield models of neural networks with N nodes and p patterns in the (thermodynamic) limit N to infinity, p constant. We study local and global properties of this limiting dynamics.