An experimental investigation was done by the use of visual observations and the electrochemical technique in order to study the appearance of hydrodynamic instabilities at low Re-axg in the gap between two coaxial cylinders, with radius ratio R-r/R-s = 0.615 and aspect ratio L/e = 24. A motor drove the inner cylinder and the outer cylinder was fixed. A Newtonian fluid (Emkarox HV45) and two non-Newtonian fluids (aqueous solutions of guar and CMC) have been used. The analysis of the evolution of the size of the Taylor vortices is carried out for Re-axg < 4.0. For Re-axg < 2 we showed that the vortices underwent a contraction phase up to Ta-g approximate to 80, and a stretching phase for Ta-g > 80. For higher Re-axg, the contraction phase vanished and the vortices progressively stretched with increasing Ta-g. A dimensionless representation was also proposed for wall friction generalized to non-Newtonian fluids following the Ostwald law.