The nonlinear theological character of microphase-separated ABA-type block copolymer melts was investigated in the context of stress relaxation experiments. Five grades of triblock copolymers were studied in step strain programs. End blocks were polystyrene and middle blocks either polybutadiene or polyisoprene. Molecular weights ranged from 61 300 to 140 000 and styrene fractions from 0.14 to 0.44. Test temperatures (90-110 degrees C) were above T-g of the styrenic microphases and below the separation temperatures of these polymers, so all were multiphase systems with each phase in the liquid state. Strain amplitudes (gamma degrees) ranged from 0.05% to 3.86%. At the highest gamma degrees, relaxation moduli dropped steadily in liquidlike fashion; at lowest gamma degrees, the stress relaxation was overtaken by a competing microstructural recovery process which caused the modulus to pass through a minimum and then increase. Results are discussed in terms of the interfacial diffuse phase (interphase), morphology, and molecular weight.