Low levels of long-chain branching (LCB) in an otherwise linear polyethylene, such as HDPE or LLDPE, are known to affect dramatically the polymer melt rheological properties. However, reliable techniques to detect and quantify LCB at these levels (i.e., <<1 LCB/1000 C) have not been available. In this work, the long-chain-branching index (LCBI) is developed for essentially linear, polydisperse polyethylenes, which are those containing a small level of LCB, such that the measured intrinsic viscosity is the same, within experimental error, to that calculated from MWD data, assuming the resins are linear. The long-chain-branching index (LCBI) is fundamentally related to the viscosity enhancement due to long-chain branching, and it is independent of molecular weight (MW) and molecular weight distribution (MWD). It is given by the relation : LCBI = n(o)(0.179)/4.8[eta] - 1, where eta(o) (P) is the zero shear viscosity at 190 degrees C, and [eta] (dL/g) is the intrinsic viscosity in trichlorobenzene at 135 degrees C. A suitable average molecular weight could substitute the intrinsic viscosity in this relation, if so desired. The numerical factors in the defining relation are derived on fundamental grounds such that the lowest value of 0.0 represents perfectly linear polyethylene. Various measures of LCB that have appeared in the literature, including the Dow rheology index (DRI) and those based on the activation energy of viscous now, are critically examined and their limitations identified. The new index proposed here overcomes these limitations, as illustrated with a vast number of examples with commercial polyethylenes. The applicability of the LCBI for distinguishing LCB levels within conventional, free-radical polymerized LDPEs is also investigated.