In this study, we present a comparative investigation of linear and branched wormlike micelles using two nonlinear rheological tools: orthogonal superposition rheology and large amplitude oscillatory shear (LAOS) rheology. The surfactants were a series of mixtures of octyl trimethyl ammonium bromide (C(8)TAB) and sodium oleate (NaOA). A transition from linear to branched wormlike micelles was obtained by either varying the relative ratio of NaOA to C(8)TAB at a fixed total surfactant concentration or by fixing the ratio of NaOA to C(8)TAB and varying the total surfactant concentration. Orthogonal superposition rheology imposes a small amplitude oscillatory shear strain over an orthogonally imposed shear flow to probe the effect of shear on the storage and loss modulus of the fluid. For both the linear and branched wormlike micelle solutions, the plateau modulus, the relaxation times, and the dynamic viscosity were all found to be sensitive to the strength of the orthogonally imposed shear rate. However, the nonlinear effects were much more pronounced for the case of the branched wormlike micelle solutions. This is likely due to a break-down of the branched wormlike micelles under flow which can be inferred from the decrease in the plateau modulus and the subsequent increase in the calculated mesh size of the entangled micelle network with increasing orthogonal shear-rate. In the LAOS measurements, both the linear and branched wormlike micelles exhibited a qualitatively similar trend in the viscoelastic nonlinearities as the strain amplitude of the imposed oscillatory flow was increased. However, the strength of viscoelastic nonlinearities, both within an oscillatory cycle and with increasing strain amplitude, of the branched wormlike micelles was found to be significantly larger than those observed for the linear wormlike micelles. Additionally, at large strain amplitudes, the Lissajous-Bowditch plots of the branched wormlike micelle solutions were found to exhibit a secondary loop resulting from a negative elastic modulus. This is indicative of a stress overshoot and likely the result of a cyclical breakdown and reformation of the underlying wormlike micelle entangled structure during an oscillatory cycle. (C) 2016 The Society of Rheology.