Due　to　R+　=　[0,　8)　being　a　group　under　Walsh　addition　?,　the　wavelet　frame　theory　on　L-2(R+)　has　been　well　developed　in　recent　years.　This　paper　addresses　wavelet　dual　frames　on　Sobolev　spaces　defined　on　R+　We　introduce　the　Sobolev　space　H-s(R+)　with　s　?　R,　characterize　(weak)　nonhomogeneous　wavelet　dual　frames　for　(H-s(R+),　H-s(R+)),　and　establish　mixed　oblique　extension　principles　for　constructing　them.