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In the presented paper dynamics of a rotating flexible composite thin-walled box-beam subjected to additional lateral to-and-for hub movement is investigated. The assumed blade spacial orientation and Circumferentially Asymmetric Stiffness laminate material configuration results in specimen twist/inplane bending/in-plane shear motions coupling. The set of partial differential equations of motion of the structure is formulated using the Hamilton least action principle. Next, performing the Galerkin discretisation and adopting the orthogonality condition these are transformed to the final ordinary differential equation. It is shown that some coefficients of the governing equation are time-varying ones. They depend on the system angular velocity as well as on the base excitation frequency. Thus, this form of the governing equation is different from the typical Mathieu-Hill's equation. Results of numerical simulations present the influence of the laminate fiber orientation angle, hub radius to beam length ratio and base excitation frequency on the dynamic stability of the system.