We have developed a sensitive method to detect very low levels of long chain branching in sparsely branched polymers and applied it to high-density polyethylene samples with broad molar mass distribution obtained by Ziegler-Natta, Phillips, and metallocene catalysis. We compare experimental dynamic moduli with predicted values. The predicted moduli, which are only valid for truly linear chains, are computed from a known molar mass distribution by the application of a modified time-dependent diffusion reptation model described in [van Ruymbeke et al., Macromolecules 35, 2689 (2002)]. Discrepancies between experimental and predicted moduli are observed at branching levels below the usual detection limit Of C-13 nuclear magnetic resonance (about I branch per 10000 carbon atoms). Our method is easier to implement and the results more clearcut than those obtained by the zero-shear viscosity method. The sensitivity is comparable with the activation energy spectrum method described in [Wood-Adams et al., Macromolecules 33, 7489 (2000)]. The use of our method is however not restricted to thermorheologically complex polymers. The interest of polymer fractionation is also demonstrated for the detection of extremely low levels of long chain branching. (c) 2005 The Society of Rheology.