The　global　stability　of　a　nonlinear　discrete　population　model　of　Volterra　type　is　studied.　The　model　incorporates　time　delays.　By　linearization　of　the　model　at　positive　solutions　and　construction　of　Liapunov　functionals,　sufficient　conditions　are　obtained　to　ensure　that　a　positive　solution　of　the　model　is　stable　and　attracts　all　positive　solutions.　An　example　shows　the　feasibility　of　our　main　results.　©　World　Scientific　Publishing　Company.