A numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted. The full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role. At weak to moderate rotation rates, a double-vortex secondary flow appears in the transverse planes of the duct whose structure is relatively independent of the aspect ratio of the duct. For Rossby numbers Ro < 100 this secondary flow is shown to lead to substantial distortions of the axial velocity profiles. For more rapid rotations (Ro < l), the Secondary flow (in a duct with an aspect ratio of two) is shown to split into an asymmetric configuration of four counter-rotating vortices similar to that which appears in curved ducts. It is demonstrated mathematically that this effect could result from a disparity in the symmetry of the convective and Coriolis terms in the equations of motion. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration and the axial velocity wumes a Taylor–Proudman configuration in the interior of the duct. Comparisons with existing experimental results are quite favourable.