Abstract: This is joint work with Yuriko Renardy (Virginia Tech). The dynamics of a viscoelastic liquid in parallel shear, driven by an initial shear stress jump, is investigated and shown to display thixotropy, yielding and unyielding behavior. The constitutive model is a combination of the partially extended convected model (PEC), modified to allow for a non-zero shear stress limit for large shear rates, and a Newtonian solvent. Thus, the concept of a yield stress is not built into the model. We assume that the ratio of retardation time to relaxation time is small, and perform asymptotic analyses of various time scales which emerge. The process of yielding reveals new solutions such as time-periodic solutions, in addition to the familiar steady shear flows. Such a yielded solution is used as an initial condition to study unyielding, together with a step-down in the applied shear stress. The subsequent dynamics again displays multiple time scales. Perturbation methods, in conjunction with direct computation of solution trajectories for the original full equations, show novel transitions back to unyielded states. The commonly observed phenomenon of the hysteretic loop in the value of yield stress versus shear rate for steady shear solutions is also retrieved.