Viscoelastic behavior, phase equilibria, and microdomain morphology in mixtures of a polystyrene-block-polybutadiene-block-polystyrene copolymer (Kraton 1102, Shell Development Co.) and a low molecular weight homopolymer were investigated. For the study, a series of nearly monodisperse polystyrenes (PS) and poly(alpha-methylstyrene)s (P-alpha-MS) with molecular weights ranging from 1200 to 9900 were synthesized via anionic polymerization, and each of the homopolymers was mixed with the block copolymer Kraton 1102. The mixtures were then characterized by means of the dynamic moduli and loss tangent using dynamic viscoelastic measurements. It was found that the solubility limits of P-alpha-MS in the block copolymer Kraton 1102 are greater than those of PS. Phase diagrams were constructed experimentally for mixtures of Kraton 1102 and homopolymer P-alpha-MS using the results of dynamic viscoelastic measurements (i.e., logarithmic plots of dynamic storage modulus versus dynamic loss modulus), which allowed us to determine the boundary between the mesophase and the homogeneous phase, and turbidity measurements, which allowed us to determine cloud point curves for liquid-liquid (macrophase) separation. Experimental results were compared with predictions made by the theory of Noolandi and co-workers. The morphological transition of the ordered microdomains as affected by the addition of homopolymer was investigated using small-angle X-ray scattering and transmission electron microscopy. Emphasis was placed on investigating the effects of molecular weight and concentration of added homopolymers on the dynamic viscoelastic behavior, phase equilibria, and morphological transition of ordered microdomains in mixtures of a block copolymer and a homopolymer.