Static pressures, mean, rms and secondary flow velocities were measured by the use of laser Doppler velocimeter with Newtonian and non-Newtonian flows which ensured laminar, transitional and turbulent flows in the eccentric annuli. Static pressure distribution with Newtonian fluid, was approximately 15% smaller than that of smooth pipe and near wall velocities deviated from the law of the wall by up to 5%. The location of maximum velocity and zero shear stress occurred at the gap center within the measurements accuracy. Secondary flows driven by the differences between the two cross-stream normal stresses (v2-w2) had a maximum value of 2.2% of the bulk velocity. With non-Newtonian flows, there was a drag reduction of up to 60% and the near wall velocities deviated from the wall so that they approached maximum drag reduction asymptote. The rms velocities decreased particularly in the radial and tangential direction which were almost one-third of their Newtonian values.