In this paper, we study the global behavior of positive solutions of the system of difference equations xn+1=A+ynyn−k,yn+1=A+xnxn−k,n=0,1,…with parameter A>0, the initial conditions xi,yi are arbitrary positive numbers for i=−k,−k+1,…,0 and k∈Z+. Moreover, we provide semi-cycle analysis of positive solutions of the above system of difference equations. We also provide numerical examples that support our analytical results.