This paper is concerned with the boundedness, persistence, and global asymptotic behavior of positive solution for a system of two rational difference equations x n+1 = A + (x n /∑ i=1 (k) y n-i ), y n+1 = B + (y n /∑ i=1 (k) x n-i ), n = 0,1,…, k ∈ {1,2,…}, where A, B ∈ (0, ∞), x -i ∈ (0, ∞), and y -i ∈ (0, ∞), i = 0,1, 2,…, k.