The present work investigates nonlinear behavior in large amplitude oscillatory shear (LAOS) of four different polymeric materials using simultaneous conventional rheometric measurements and particle-tracking velocimetric observations. In contrast to most studies in the literature that treat nonlinearity in LAOS in steady state, we emphasize by the present four examples that nonlinearity in LAOS often arise in complex fluids due to time-dependent rearrangement of their microstructures in response to LAOS. Consequently, no correlation is obvious between strain dependence of the steady-state stress response and the time-dependent characteristics of the steady-state response. For instance, a highly viscoelastic material made of nano-sized polybutadiene particles exhibits homogeneous deformation and an approximate sinusoidal wave despite strong strain softening. In a second example, a well-entangled polybutadiene solution becomes inhomogeneous over time, and the corresponding nonlinearity (i.e., strain softening) took a finite time to develop to its fullest. In the example of wall slip of a monodisperse entangled polyisoprene melt, contrary to the literature claim that even harmonics would emerge, we show that the stress response only involves odd harmonics in the absence of any edge fracture. Last, a polydisperse poly(dimethyl siloxane) melt experiences homogeneous LAOS without displaying significant higher harmonics in the absence of any edge failure. In contrast, the Fourier transform analysis shows that meniscus failure is responsible for the emergence of higher harmonics including some even ones. (C) 2009 The Society of Rheology. [DOI: 10.1122/1.3193713]