The Soret and Dufour effects on the peristaltic transport of a conducting Casson nanofluid in a flexible channel are studied. The influence of dissipation and Joule heating are also discussed. The governing equations are simplified by using a long wave length and small Reynolds number approximations. The analytical solutions for stream function and axial velocity are obtained. Moreover, the Runge–Kutte-based shooting method is utilized to solve the coupled energy and concentration equations. The impact of important parameters on the flow is explained using graphs for both Newtonian and Casson fluid cases. It is observed that the Casson fluid has more velocity than the Newtonian fluid in the middle of the channel and the situation is reversed at the channel walls. Further, a higher temperature is noted for Casson fluid than for Newtonian fluid throughout the channel, whereas concentration shows the opposite behavior. © Springer Nature Switzerland AG 2019.