Nowadays the theory, methods and techniques concerning the application of mathematical models are wide used. Nevertheless such problems as a quality estimation of multi-criteria models, an analysis and classification of applied models, as well as justified selection of task-oriented models are still not well investigated. The importance of the problem increases when a research object is described not via a single model, but with a set or a complex of multiple-models including models from different classes or combined models such as combined analytical–simulation models, logical-algebraic ones, etc. Aforementioned problems are the primary research objects of the quality control theory of mathematical models and multiple-model complexes. The description of main elements of this theory is the primary goal of the paper. The implementation of this theory is connected with the information fusion multiple-models area