On the basis of known mathematical models describing vibrations in the gas flow of a bluff body with one degree of freedom, a model of vibrations of a body with two degrees of freedom is obtained. The Krylov-Bogolyubov method is applied. Equations for slowly varying amplitudes and phase shift of vibrations are obtained. It turned out that the differential equations written for the squares of dimensionless amplitudes of translational and rotational vibrations coincide with the well-known Lotka-Volterra equations describing competition between two species of animals that eat the same food. In a wind tunnel, the change of modes of vibrations of the bridge segment predicted by a mathematical model is studied.