The paper investigates peristaltic flow of a Power-law fluid in contact with a Jeffrey fluid in an inclined channel with permeable walls under long wavelength and low Reynolds number approximations. Power-law fluid is considered in the core region and Jeffrey fluid in the peripheral region. Expressions for the shape of interface between the two fluids and the pressure rise are obtained. It is observed that an increase in permeability parameter increases the thickness of the core layer in the channel. It is also observed that pressure rise increases with decrease in the Jeffrey parameter. © 2015 Faculty of Engineering, Ain Shams University