Abstract: The time dependent Lotka-Volterra mutualistic system
ẋ_i=x_i(r_i(t)+∑_j=1ⁿa_ij(t)x_j),(i=1,…,n) be considered under the assumption that r_i(t) and a_ij (t) are ω-periodic functions. A set of easily verifiable sufficient conditions are given which gurantee the global asymptotic stability of positive ω-perodic solution of system (1). When r_i(t), a_ij(t) are constants, the conditions are coincident with the necessary and sufficient condition that the positive equilibrium (if there exists) is global asymptotic stable.