With a rotary rheometer, various methods were used to determine the characteristic relaxation times for a commercial polydimethylsiloxane (PDMS), and their consistency and relation to the linear relaxation spectrum were examined. The experimental damping functions of the step deformation of the PDMS, a polymethylvinylsiloxane, and a high-density polyethylene were compared with predictions of the Doi-Edwards theory and Marrucci model; the effect of wall slip on the damping function data is discussed, and the appearance of stress peaks due to material instability as the strain increased above a critical value is detailed. Through the application of a previously proposed stress decomposition method to the data of large-amplitude oscillatory shear for the PDMS sample, the relationship between the generalized elastic modulus [G'(N)((omega,gamma)] and the shear relaxation modulus [G(gamma,t)] was investigated. In the linear and initial nonlinear regimes, as the angular frequency (omega) increased, G'(N)(omega,gamma) approached G(gamma,t) on the timescale t = 1/omega, where t is the time. (C) 2008 Wiley Periodicals, Inc.