In this research the stability of Taylor-Couette flow of Newtonian and drag reducing fluids was experimentally studied. The primary concern was to investigate the effect of added polymer on the critical Taylor number. The polymer chosen in this study was polyacrylamide, xanthan gum and polyacrylic acid and the solvent was 1:1 mixture of glycerine and distilled water. The concentration was in the range of 0-0.5 of the coil overlap concentration. The result showed that the qualitative characteristics of transition from the stable Couette flow to the turbulent flow was found to be similar to that of Newtonian fluid. In the cases of polyacrylamide and xanthan gum solutions, the critical Taylor number decreased as the polymer concentration increased. Some polyacrylic acid solutions showed increase in the critical Taylor number. The Couette flow was stabilized by the added polymer when the solvent viscosity was used in determining the critical Taylor number regardless of polymer type. This implies that the wall layer of turbulent pipe flow should be stabilized and hence manifest drag reduction. By using a dilute solution theory, the second normal stress difference coefficient was estimated. It was found that the ratio of second to first normal stress difference coefficients was negative and in the range of 0.0-0.2, and was closely related to the flexibility of polymer chain. It was also found that even a very weak shear rate dependency of viscosity could play an important role in determining the stability of Couette flow.