In this paper, the stability of adaptive structures during steady periodic motion is discussed. The adaptive structure in this paper is a two-dimensional variable geometry truss which consists of N bays. The structure controlled by a periodic optimum controller converges into "2-link mode" in which N-1 bays are the same shape. The results of numerical calculation show that 2-link mode satisfies the optimal condition. Periodic optimum controller has other possibility that the structure converges into a locally optimum mode. To confirm that the system does not stay the locally optimum mode, the stability is examined with eigenvalues and eigenvectors that are derived from a linear system. The results show that the structure in 2-link mode has global stability to keep the steady motion. It is also shown that the other locally optimum modes are unstable neutral points.