Solutions of the Navier–Stokes equations for flow in a curved channel have previously been computed [Bottaro, J. Fluid Mech.251, 627 (1993)] and the spatial development of the Dean flow is available at different supercritical Reynolds number. In this work the viscous instability of local longitudinal vortex structures (obtained from the nonlinear simulations) is investigated, with a focus toward the secondary instability of Dean vortices. Such a secondary instability takes the form of streamwise traveling waves. High‐frequency waves are termedtwistingwaves, low frequency are definedundulatingwaves. Instead of performing analyses in which the basic flow in the cross section is two dimensional, significant shear profiles alongyandzare considered as base flows at constantxbefore the establishment of a fully developed state. Thus one is able to discover that thetwistinstability is of shear type and is caused by inflectional spanwise profiles of the streamwise velocity component. Sinuous waves are always preferred to varicose waves, and the latter mode of instability is destabilized only at large Reynolds numbers.Undulatingwaves are related to normal profiles of the streamwise velocity; this type of secondary instability is of centrifugal origin. Results of the analyses for both types of waves are in good agreement with experiments.