Metallocene catalysts are known to produce homogeneous random polyolefin copolymers with narrow molecular weight distribution and controlled long/short-chain branching. Two such linear low-density polyethylenes were studied by using both constant-stress and capillary rheometry, in order to assess their rheological and processing behavior, as well as to identify critical conditions for the onset of flow instabilities. It was found that these polymers are thermorheologically complex liquids, apparently due to the presence of long-chain branching. Compared with conventional linear low-density polyethylenes, these metallocene polyethylenes exhibit quite unusual behavior in capillary flow, not previously reported to our knowledge. Specifically, we have encountered long transients in start-up of capillary experiments, and in some cases, the capillary reservoir had to be loaded several times before a steady-state pressure was obtained. In addition, we found that these polymers slip at shear stresses higher than about 0.05 MPa. This critical value is much smaller than the critical value of 0.10 MPa reported for other conventional polyethylenes. A simple qualitative model is proposed to rationalize these findings. It suggests that the molecular mechanism of slip is dominated by a competition between flow-induced chain detachment from the wall and disentanglement of the chains in the bulk from those attached to the wall.