By using the continuation theorem of coincidence degree theory, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay Lotka-Volterra competition system and the periodic state dependent delay Lotka-Volterra competition system dt dui(t) ui(t)[ri(t) aii(t)ui(t) n∑j1ji aij(t)∫oTij Kij(s)uj(t s)ds],i 1, 2……, n, and the periodic state dependent delay Lotka-Volterra competition system dt dui(t) ui(t)[ri(t) aij(t)ui(t) n∑j1ji aij(t)uj(t τj(t,u1(t),……,un(t)))],i 1, 2,……, n, where ri, aii>0, aij 0(j i, i, j 1, 2, …, n)are continuous ω-periodic functions, Tions, Tij (0,∞)(j i, i, j 1, 2, …, n), Kij C(tij, 0, (0,∞)), ∫0 Tij Kij (s) ds 1(j i, i, j 1, 2, …,n), τi C(Rn 1, R), and τi(i 1, 2, …, n) are ω-periodic with respect to their first arguments, respectively.