Rotational motions, or vorticity, can be created within a fluid domain by two mechanisms: baroclinic torque and viscous-shear torque. Both baroclinic and viscous-shear torques require the presence of fluid-density gradients. It is shown that vortical motions in the surface roller of a bore are created by baroclinic torque acting along the front face of the bore; this baroclinic torque is caused by the dynamic-pressure gradient along the air-water interface. On the other hand, vortical motions in an internal bore, with a small density difference between the upper and lower fluids, are generated by baroclinic torque caused by the static-pressure gradient along the interface of two fluids. Vorticity generated in an internal bore has the opposite rotation to that of a bore in the air-water environment. In both cases, the viscous-shear torque plays an insignificant role in the creation of vorticity.