International crises and major ongoing internation disputes are a central topic of concern for everyone. This project provides scientific theoretical underpinnings to our understanding of the recurrence of major international disputes. The goal is to study mathematical representations of dispute sequences or histories by drawing together the work of the principal researchers in international relations and embedding them in a framework that emphasizes common ties, interests, interconnections, and relationships among nations.. By analytic and computer explorations, attempts will be made to predict, for a sequence of disputes, who will be a party to each dispute, what will happen in each dispute, and how the outcome and details of each dispute will affect the relationships among the nations involved. These predictions will then be used to examine a number of major questions current in the international relations literature and develop empirical tests using several of the datasets that have been compiled by the National Science Foundation's project on Data Development for International Research. This project goes beyond previous studies of internation conflict because it examines dispute sequences, allows different nations to move in and out of disputes from one time period to the next, and brings to the forefront the important influence of relationships among nations.