he physicist and Nobel laureate Ilya Prigogine states that "our understanditig of nature is undetgoitig a tadical change towatd the multiple, the temporal, and the complex. Curiously, the itnexpected complexity f'oitnd in nature has not led to a slowdown in the progress of science, but on the contrary to the emergence of new conceptual structures that now appear as essential to our understanding of the physical world" [11]. We believe the challenges posed by complex systems arise primarily from the use of conceptual structures that wotked well for static systems but do not work as well for more dynamic systems. We therefore propose new conceptual structures based on a different metaphysical view of the nature of complex systems.In this article we use the word system to denote a system in the t eal world (for example, a corporation, a biological system, a legal system), and application to denote the representation of a system. Object and entity are used interchangeably, and may refer to an object, classifications of objects, or relatiotiships between objects.Current approaches to complexity presume an ontology of objects and relationships, sometimes explicitly including processes and, in science, sometimes explicitly including observers. They reptesent these in various ways. Objects and their relationships are usually declared in data. Procedural aspects rarely are, and instead are encoded as software with certain branching point values (parameters) possibly defined as data. Semantic, hypersemantic, object-oriented, and functional conceptual data modeling approaches are evolving to represent "business knowledge" such as heuristic rules and temporal characteristics of objects as data [7,10]. We agree that far more information about a system can usefully be represented in data rather than in software, but believe there is a fundamental need to identify new conceptual structures that are more stable than objects, relationships, rules, or processes and are therefote mote appropriate as the basis for lepresenting and comprehenditig complex systems.Ultra-Structure is a general theory regarding the improved representation of complex rules. It was originally derived from the linguist Noam Chomsky's work on transfortiiational grammar. In applying Chomsky's theory over the past nine years to businesses and other complex systems, we have substantially modified his theory. Ultra-Structure is based oti two key hypotheses:1) The Ruleform Hypothesis: Complex system structures and behaviors are generated by not-necessarily-complex processes; these processes are generated by the animation of operating rules. Operating rules can be grouped into a small number of classes, whose form is prescribed by ruleforms. While the operating rules of a system change over time, the ruleforms remain constant, A well-designed collection of ruleforms can anticipate all logically possible operating rules th^ir coMMUHlCATiails ov THI ACM |aiuiarv 199.'i/Vnl..1H. No. I 103