An investigation was conducted to identify and characterize the relaxation spectrum of polymer melts from transient capillary rheological data. System identification techniques using an iterative prediction-error minimization (PEM) method were applied to isolate the viscoelastic melt response from the apparatus dynamics. Parameters for linear time invariant (LTI) models of varying complexity were estimated using capillary rheology data across a range of temperatures and shear rates using the principle of time-temperature superposition. Melt capillary rheology data for polystyrene was found to exhibit viscoleastic behavior. Subsequently, three viscoelastic constitutive models were then implemented and their model coefficients directly fit using optimization techniques. The implemented methods provided useful relaxation behavior from melt capillary rheology data while also explaining much of the residual error in the purely viscous response as traditionally fit to the Cross-WLF model. POLYM. ENG. SCI., 54:2824-2838, 2014. (c) 2014 Society of Plastics Engineers