Reproducing　systems　in　L2(R)　such　as　wavelet　and　Gabor　dual　frames　have　been　extensively　studied,　but　reducing　systems　in　L2(R+)　with　R+=(0,∞)　have　not.　In　practice,　L2(R+)　models　the　causal　space　since　the　time　variable　cannot　be　negative.　Due　to　R+　not　being　a　group　under　addition,　L2(R+)　admits　no　nontrivial　shift　invariant　system　and　thus　admits　no　traditional　wavelet　or　Gabor　analysis.　However,　L2(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　L2(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　L2(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　ba　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.　©　2023,　The　Author(s),　under　exclusive　licence　to　Malaysian　Mathematical　Sciences　Society　and　Penerbit　Universiti　Sains　Malaysia.