Reproducing　systems　in　L-2(R)　such　as　wavelet　and　Gabor　dual　frames　have　been　extensively　studied,　but　reducing　systems　in　L-2(R+)　with　R+　=　(0,　8)　have　not.　In　practice,　L-2(R+)　models　the　causal　space　since　the　time　variable　cannot　be　negative.　Due　to　R+　not　being　a　group　under　addition,L-2(R+)　admits　no　nontrivial　shift　invariant　system　and　thus　admits　no　traditional　wavelet　or　Gabor　analysis.　However,　L-2(R+)　admits　nontrivial　dilation　systems　due　to　R+　being　a　group　under　multiplication.　This　paper　addresses　the　frame　theory　of　a　class　of　dilation-and-modulation　(MD)　systems　generated　by　a　finite　family　in　L-2(R+).　We　obtain　a　parametric　expression　of　MD-frames,　and　a　density　theorem　for　such　MD-systems　which　is　parallel　to　that　of　traditional　Gabor　systems　in　L-2(R).　It　is　well　known　that　an　arbitrary　Gabor　frame　must　admit　dual　frames　with　the　same　structure.　Interestingly,　it　is　not　the　case　for　MD-frames.　We　prove　that　an　MD-frame　admits　MD-dual　frames　if　and　only　if　log(b)　a　is　an　integer,　where　a　and　b　are　dilation　and　modulation　parameters,　respectively.　And　in　this　case,　we　characterize　and　express　all　MD-dual　generators　for　an　arbitrarily　given　MD-frame.　Some　examples　are　also　provided.