Peristaltic flow due to the transverse deflections of the walls of the curved channel is investigated when the inertial effect is negligibly small and the wavelength is sufficiently long compared with the channel width. Theoretical results are presented for the stream function, the flow velocity and the pressure. Theoretical criteria of reflux and of trapping are obtained. The pressure-flow characteristic is found to be linear, and its slope slightly increases with an increasing channel curvature. Reflux near the outer wall is stronger than near the inner wall. The trapped bolus of fluid comprises 2 asymmetrical parts ; the outer one grows but the inner one diminishes as the channel curvature is icreased. Reflux, and trapping as well, occurs in the curved channel over wider ranges of time-mean flow and of amplitude ratio than in the straight channel.