The present invention relates to the invention relates to an assembly of a dual lumen tubing as described above and a dual bore connector as described above having a first flow conduit along the first lumen and the first bore, and having a second flow conduit from the second bore, via a circumferential groove and along the second lumen. Such an assembly may be used in connection with an extracorporeal circuit of a haemodialysis machine or an infusion set.