The non-linear viscoelasticity of concentrated solutions and glasses of soft starlike micelles has been studied by large-amplitude oscillatory shear (LAOS). The non-linear response has been analysed using current schemes of Fourier transform (FT) rheology, and its character has been determined by the phase of the third harmonic contribution to the stress. The limitations of FT rheology and related analysis methods are discussed, and an alternative method is presented that takes into account all the higher harmonics. This method reveals a strain-hardening character of intracycle non-linearities at large strain amplitudes for all volume fractions. We also show that, although the relation of LAOS with steady shear measurements works qualitatively, due to inherent limitations of LAOS, steady shear data cannot be reproduced quantitatively.