Complex frequencies and mode shapes are evaluated and presented for a guyed vertical axis wind turbine to detect any dynamic instability for a given speed of rotation. The equations of motion are developed in the rotating system of axes of the rotor to eliminate the time dependent terms. These equations take into account gyroscopic effects by evaluating the Coriolis and Circulatory (softening) matrices. The guys are replaced by nonlinear springs. The geometric stiffness matrix is also considered by performing a nonlinear static analysis that includes centrifugal effects and gravity loads, as well as compression from the vertical component of the guys. A reduction of the dynamic degrees of freedom is performed using the Rayleigh–Ritz technique. The complex frequencies and mode shapes are obtained using the QR algorithm. A program developed on a microcomputer was used to evaluate the dynamic instabilities of the ÉOLE Project. These results are described in the following paper.Key words: Vertical axis wind turbines, guys, complex frequencies, complex mode shapes, centrifugal forces, Coriolis forces, numerical software.