The proposition is made that simple time-temperature superposition should not be valid for block copolymers exhibiting multiple mechanical transitions; and an explanation of the time temperature behavior, which is more consistent with the behavior of the individual phases, is presented in terms of an equivalent mechanical model. Based on this model, a method for generating time-temperature shifts, which depend on the experimental time as well as temperature, is developed. This method can easily be extended to any mechanical model and should be valid for polymer composites in general. The storage and loss compliances of three benzene cast polystyrene/l,4-polybutadiene/polystyrene triblock copolymers with different compositions were measured between -85 and 90[degrees]C over a frequency range from 0.1 to 1000 Hz. The measurements suggest the presence of four relaxation processes. Two, the polystyrene and polybutadiene glass transitions, are treated according to the method of time-temperature superposition referred to above. Anomalous behavior appearing between the two glass transitions is attributed primarily to a temperature dependent interlayer between the two phases and can be treated as a compositional change in the composite. Entanglement slippage in the rubbery matrix also contributes to the total relaxation. The apparatus used for these experiments is an extensively modified model of the Miles shear generator. This improved version offers large experimental frequency and temperature operating ranges.