In several polymer production and processing technologies diffusive mass transport with convection due to elongational flow is encountered. Examples of such processes are film-blowing, fibre-spinning and polymer strand devolatilization. The classes of problems considered in this paper are steady-state and - closely related to them - unsteady-state convection-diffusion problems with elongational flow. The question treated is as to what influence the type and strength of the elongational flow have on the convective-diffusive mass transport inside the polymer phase.