A. A. Gourchenkov SAMS , Vol. 40 , 01.2001 , p. 447-458, language: английский ISSN 0232-9298  Аннотация One of the important problems in system theory and engineering sciences is the modelling problem, directly connects to both the well-known reduction principle of stability theory by A. M. Lyapunov and comparison method. The main goals are the development of valid mathematical model; distinction between essential factors and non-essential ones; the estimations. In engineering practice the simplified models have been used. Partly it is caused by the absence of exact theory as well as regular engineering techniques (N. N. Moiseev). This paper presents the theoretical basis of new model for an unsteady flow of viscous incompressible fluid in a rotating slot. The slot is formed by two parallel plates. The distance between plates is fixed. The slot with viscous fluid is rotated around axis which forms angle$\alpha$ ($0 < \alpha < \pi/2$) with the plane of the plates. The unsteady flow is induced by the motion of the upper and lower plates. The exact solutions of Navier-Stokes equations are presented and discussed. Some characteristics of boundary layers are investigated.  Ключевые слова вязкая жидкость, вращающиеся системы