Large amplitude oscillatory shear flows of polymer melts between parallel plates may exhibit complicated nonperiodic responses characteristic of quasiperiodicity or chaos. This complex time dependence is related to the wall slip exhibited by these materials. We use simple models for the fluid elasticity and slip to theoretically and computationally study the nonlinear dynamics of melts in oscillatory shear. The results indicate that both fluid elasticity and adynamic(e.g. memory‐slip) model for the wall slip are necessary for nonperiodic dynamics to occur. Furthermore, when elasticity and a dynamic slip model are coupled, many qualitative features of the dynamics observed in the experiments can be reproduced. In particular, asymmetric periodic responses exhibiting even harmonics are found, as well as quasiperiodic and chaotic motions. Particularly interesting is the prediction ofmultiplestableperiodicmotionsfor a given set of parameters, depending on initial conditions. As a special case, the model reduces to the classical Duffing equation of nonlinear vibration theory. The existence of complex dynamics is robust with respect to changes in both the constitutive model chosen and the details of the wall slip model.