The time constant, τ, signifying the onset of non-Newtonian behavior of polymer solutions is known to be a function of mass concentration, C, molecular weight, M, temperature, T, and zero shear viscosity, η0. Williams' theory predicts that the time constant is also affected by the solvent character. To study the predicted effect, the time constants of poly(methyl methacrylate) solutions in chlorobenzene (good solvent) and m-xylene (poor solvent) were experimentally determined. It was found that the ratio of the time constant to the Rouse relaxation time was a function of the combined variable CM. For all values of CM, both the time constant and the ratio of the time constant to the Rouse relaxation time were larger in a poor solvent than in a good solvent. This behavior may be attributed to the relatively stronger attractive interpolymer molecular forces present in solutions in poor solvents. As the temperature is raised the poor solvent becomes better and the ratio of the time constant to the Rouse relaxation time is found to become independent of solvent character.