Summary: An extended system was introduced in [P. J. Aston, A. Spence and W. Wu, SIAM J. Appl. Math. 52, No. 3, 792-809 (1992; Zbl 0764.34033)] for the computation of travelling wave (or rotating wave) solutions of nonlinear ODE’s with \(O(2)\) symmetry. We show that the stability of the travelling waves can be determined by the eigenvalues of the extended system in a way similar to the situation for the stability of usual steady-state solutions.