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This thesis deals with a new paradigm for Complex Systems of an evolving structure which is referred to as Structure Evolving Systems (SES). A wide range of challenging issues are concerned involving the evolution of structure and associated system properties through different forms of complexity and these are closely related to integrated system design. The thesis deals specifically with issues related to the representation of t.he different forms of structural evolut.ion. A number of new forms of evolution are introduced expressing differ- ent design problems, such as Design Time Evolution, Dimensional Graph Evolution, Life Cycle Structural Evolution, Cascade Design Evolution. The main objective is to develop a representation framework for the different types of structural evolution which will offer the proper set up for the study of evolution of structural characteristics and system prop- erties. The main part of the study is concerned with the development of representation of the System Structure Evolution in terms of a chain of models as a way to represent the different stages of Design Time Evolution which involves the modelling of a system from the very early stages up to the late stages when detailed descriptions are used for design. The development of nested representations for the case of Single-Input, Single-Output Systems is presented here based on the theory of continuous fraction expansion of rational functions and then examine property evolution within the naturally generated nests. A " natural" way for generating chains of models of variable complexity is introduced based on a frequency domain approach using the infinite Laurent expansion. This approach provides a natural link to the problem of partial realization, which in turn provides a useful set up for tpe study of evolution of system structure and properties. Within the framework of Cascade Design Evolution, we develop a generic representation describing the evolution from the aggregate system to the composite system. This involves the development of the new concept of COTY1- pleteness of composition. We also clarify the notion of deviations from completeness ,; , develop a representation of the noncomplete composite system in terms of standard control concepts and tools. This provides the fundamentals for the development of a control theory based approach for designing composite systems with desirable structural characteristics. Within this framework, completeness is expressed as output feedback and deviations from completeness as input and output decentralized squaring down. This representation pro- vides control concepts and tools which allow the structuring of linear composite systems to be addressed as a problem of generalised control design. The present work contributes to the development of the theory of the new system paradigm and studies the evolution of a number of system properties under different types of system structure evolution.