Large amplitude oscillatory shear experiments were carried out on a polyurethane melt using a sliding plate rheometer incorporating a shear stress transducer. Three types of nonlinear behavior are described: periodic, quasi‐periodic, and chaotic, and common methods for characterizing these types of behavior are given. Spectral analysis is shown as the best way to distinguish between each type of behavior. Attractor reconstruction from chaos theory is introduced as a way to understand the dynamics of a system from only one dependent variable. At a low strain amplitude and frequency the behavior of the polyurethane melt is periodic but at higher amplitudes the response becomes quasi‐periodic.