Arranging efficient operation of the fleet of induction motors (IM) in non-ferrous metallurgy is a large-scale technical and economic problem. In scientific aspect, the problem is being solved in the framework of two research lines: in developing criteria for the efficient operation of the branch IM fleet and towards the development of methods and tools for implementing the IM fleet efficient operation. The article presents the results of the authors’ work in the mentiond areas. The basis for developing criteria for efficient operation is modeling of current operational states, taking into account the IM operational aging processes. The existing methods and models are poorly focused on fixation of the changes caused by operational aging. There exists a demand for special methods and tools for modeling the IM operational conditions. A mathematical model based on Kolmogorov equations is one of these tools. The system graph and equations of the mathematical model are given. An example of a practical calculation of the no-failure operation probabilities at different rates of repair operations is given. It is stated that the offered mathematical model can serve as an instrument for developing criteria of the IM pool efficient operation. The system of periodic operational diagnostics is ment to be a key element in enhancement of the IM fleet operation efficiency. A topological method worked out for the problems of operational diagnostics is focused upon analyzing the dynamics of operational changes taking place in the IM vector space. The matrix of current deviations is a medium of objective and reliable information about the current IM technical condition. Matching the matrices of current and limiting deviations allows us to make several essential conclusions concerning the IM technical state. The reported study was funded under as a part of state assignment (project number, FSWF-2020–0019), as well as at the expense of RFBR (project number, 20-01-00283).