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Average conditions are obtained for the permanence of a discrete bounded system with Holling type II functional response u(n+1)=u(n)exp{a(n)-b(n)u(n)-c(n)v(n)/(u(n)+m(n)v(n))}, v(n+1)=v(n)exp{-d(n)+e(n)u(n)/(u(n)+m(n)v(n))}. The method involves the application of estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.