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In the activities of the Dutch Global Dynamics project group, much attention has been paid to studies of the world models of Forrester and Meadows. The first part of the results of a thorough analysis of the ultimate version of the World3 model is discussed. It is argued that the capital and resource sector plays a leading part in the model and that the behavior of growth, followed by decline, is embedded in only a few of the assumptions included in this sector of the model. Subsequently, a more profound and mathematical analysis is discussed, with a view to understanding the sector's behavior in greater detail and illustrating the usefulness of a number of methods well known in system theory, which may be applied more generally if insight into a model's behavior is required. The paper is the first in a series in which the analysis of other sectors of World3 and the interplay between the sectors will be discussed.