Abstract: A shortout analytic method of stability in Strong nonlinear autonomous system is introduced into stability analysis of the themohaline double-diffusive system.Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions.For linear periodic solution in infinitesimeal motion the existence range of monotomic branch and oscillatory branch are outilined.The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value μ_c in this case of 0<r_s-r_sc<<1. The stability conclusions under different direction of vortex are drawn out .