Master curves of the small strain and dynamic shear modulus are compared with the transient mechanical response of rubbers stretched at ambient temperature over a seven-decade range of strain rates (10(-4) to 10(3) s(-1)). The experiments were carried out on 1,4- and 1,2-polybutadienes and a styrene-butadiene copolymer. These rubbers have respective glass transition temperatures, T-g, equal to -93.0, 0.5, and 4.1 degrees C, so that the room temperature measurements probed the rubbery plateau, the glass transition zone, and the onset of the glassy state. For the 1,4-polybutadiene, in accord with previous results, strain and strain rate effects were decoupled (additive). For the other two materials, encroachment of the segmental dynamics precluded separation of the effects of strain and rate. These results show that for rubbery polymers near Tg the use of linear dynamic data to predict stresses, strain energies, and other mechanical properties at higher strain rates entails large error. For example, the strain rate associated with an upturn in the modulus due to onset of the glass transition was three orders of magnitude higher for large tensile strains than for linear oscillatory shear strains. (C) 2011 Wiley Periodicals, Inc.* J Polym Sci Part B: Polym Phys 49: 1195-1202, 2011