The flow properties for 300 kg/m 3 solutions of four-arm, star-branched random and block styrene-butadiene-styrene copolymers in n-butylbenzene are presented. The viscosity, η, first and second normal stress differences, N 1 and N 2, and the steady sher compliance, J, were determined as a function of the shear rate from cone-plate shearing data obtained with a stiffened Model R17 Weissenberg Rheogoniometer. The normal stress differences were determined from total normal force and plate pressure distribution data. Four sensitive, miniature, variable-capacitance pressure transducers mounted in the 7.4-cm plate with their approximately 2.4 mm in diameter pressure-sensing diaphragms flush with the plate surface provided data for the pressure distribution on the plate. In general, the data extend from the zero shear-rate viscosity region somewhat into the shear thinning region. Based on limited data, the zero shear viscosities for the random copolymers increased with ( M 3) 3.2, whereas those for the 28% block and 38% block polymers increased with ( M w) ⪢;6, respectively. The latter high exponents are believed to be a consequence of a network with junctions formed by dispersed phase polystyrene block domains. The sign for N 2 was opposite that of N 1 and the ratio N 2/ M 1 for all of the star copolymers averaged –0.214 with a standard deviation of 1.5%. This value is within ±1% of the ratios for tetrachain polybutadienes and polystyrenes and is significantly lower than the –0.29 for linear polybutadiene and polystyrene solutions in normal butylbenzene. The N 2/ N 1 ratio did not vary significantly over the shear-rate range investigated.