Summary: The problem of peristaltic transport of a fluid with variable viscosity through the gap between concentric uniform tubes, such that the inner tube is rigid and outer tube with sinusoidal wave travelling down its wall, has been investigated under zero Reynolds number, and long wavelength approximations. The velocity field in the gap, relations between the pressure gradient and flow rate and that between the friction forces on the inner and outer tubes and the flow rate are obtained in terms of viscosity parameter, radius ratio and the degree of occlusion. The peristaltic pumping and augmented pumping are discussed with the physical parameters of interest.