In　this　paper,　we　investigate　entanglement　between　two　two-level　atoms　when　they　simultaneously　interact　with　a　single-mode　thermal　field　in　the　strong-coupling　regime.　We　show　that　a　slight　detuning　between　the　atomic　transition　frequency　and　the　field　frequency　might　cause　high　entanglement　between　the　atoms　More　interestingly,　if　we　choose　the　detuning　appropriately,　both　atoms　would　somehow　get　entangled　even　when　both　atoms　are　initially　in　the　excited　state.　(C)　2010　Elsevier　B　V　All　rights　reserved