The decay of swirl and the associated axial and radial velocity perturbations are analyzed for laminar tube flow with surface mass transfer. The initial swirl distribution is that corresponding to a fully developed flow characterized by injection or withdrawal of fluid having both circumferential and radial components of velocity. Consideration is also given to swirling flows in impermeable tubes, and new results are obtained by specializing the general solution for the case of surface mass transfer. Numerical results are presented for a range of values of the mass transfer Reynolds number. Among the findings, it is observed that at the higher rates of fluid injection, the decay, of the swirl requires a much longer length of run than does the decay of the axial and radial velocity perturbations.