This thesis presents the structural organization, theoretical foundations and basic application principles of Triune Continuum Paradigm, an original paradigm applicable to object-oriented modeling. The paradigm defines a metamodeling structure efficient in the scope of general system modeling, in particular for object-oriented frameworks. This structure is rigorous and at the same time flexible. It allows the definition of formal ontologies for various specific object-oriented frameworks, for example for Unified Modeling Language (UML) or for Reference Model of Open Distributed Processing (RM-ODP is an ISO/ITU standard). Thus different existing frameworks, like UML or RM-ODP, can benefit from the logical rigor, internal consistency, interpretation coherency, formal presentation and solid theoretical foundations of the defined paradigm. Adoption of this paradigm allows the resolution of crucial problems existing in these different object-oriented frameworks. The paradigm is formally presented and realized in a computer-interpretable form on the example of ontology describing the RM-ODP conceptual framework. Thus the paradigm realizes an important result that was never achieved previously: a single consistent formalization of the RM-ODP standard conceptual framework. This formalization presents a concrete example of formal ontology for general system modeling. The paradigm is also applied on UML. This application allowed the presentation of theoretical foundations that are necessary for the understanding and definition of the UML metamodel. This thesis is useful to readers who are interested in the fundamentals of system analysis. It can be particularly interesting to the UML semantics specialists, to the RM-ODP experts, and to ontological engineers.