For　a　kind　of　fractional　programming　problem　that　the　objective　functions　are　the　ratio　of　two　DC　(difference　of　convex)　functions　with　finitely　many　convex　constraints,　in　this　paper,　its　dual　problems　are　constructed,　weak　and　strong　duality　assertions　are　given,　and　some　sufficient　and　necessary　optimality　conditions　which　characterize　their　optimal　Solutions　are　obtained.　Some　recently　obtained　Farkas-type　results　for　fractional　programming　problems　that　the　objective　functions　are　the　ratio　of　a　convex　function　to　a　concave　function　with　finitely　many　convex　constraints　are　the　special　cases　of　the　general　results　of　this　paper.　(C)　2008　Elsevier　Ltd.　All　rights　reserved.