Wavelet　and　Gabor　frame　sets　on　the　real　line　have　been　extensively　studied.　Due　to　it　not　being　a　group　under　addition,　the　half　real　line　admits　no　traditional　wavelet　and　Gabor　frames　as　the　real　line.　In　this　paper,　we　introduce　a　class　of　dilation-and-modulation　frame　sets　(　MD-frame　sets)　on　the　half　real　line.　We　characterize　MD-frame　sets　and　MD-tight　frame　sets　and　obtain　some　sufficient　conditions　for　MD-tight　frame　sets.　In　particular,　we　prove　that　MD-tight　frame　sets　must　be　bounded,　but　MD-frame　sets　need　not　be　bounded.　Some　examples　are　also　provided.