The linear stability of two axially superposed immiscible fluids between two rotating coaxial cylinders is studied. The fluids are assumed to have equal density but different viscosities. The effect of viscosity ratio of the two fluids on the condition for onset of instability is studied. The critical Taylor number in the less viscous fluid for onset of instability is obtained as a function of the viscosity ratio. The two limiting values of this curve correspond to critical Taylor numbers of the one fluid configuration with height of fluid column either equal to that of the less viscous fluid or equal to the sum of those for both liquids. It is found that the variation of the critical Taylor number with viscosity ratio is small when the heights of the fluid columns are large compared to the gap between the cylinders but is significant when the heights are comparable with the gap. The marginal state is found to be stationary.