Weingarten and Linear WeingartenType Tubes with Darboux Frame in E ³

In this study, we have found that the tube surface with Darboux frame is also Weingarten surface in the Euclidean 3-space E ³ . Then we get the necessary and sufficient conditions for being (H, KII ), (K, KII ) types Weingarten tube surfaces with Darboux frame. In addition to that we have proved that there are no (H, KII ) and (K, KII )-types linear Weingarten surfaces with Darboux frame. Here K, KII and H are Gauss curvature, second Gauss curvature and mean curvature of tube surface, respectively.