The region of acceptable quality in the space of operating parameters of a coating process is usually bounded by various coating defects. An important limit of the slot coating process is the low-flow limit. It is the maximum web speed at a given film thickness and distance between coating die and web (coating gap); equivalently, the minimum film thickness at a given web speed and coating gap; again equivalently, the maximum gap at a given film thickness and web speed at which the coating bead remains stable. The condition that defines this limit is a force balance at the downstream meniscus of the coating bead, where the coated layer is carried away by the web translating past the die. Although most of the liquids coated industrially are polymeric solutions, dispersions, or both, that are not Newtonian, most previous investigations of the low-flow limit in slot coating dealt with Newtonian liquids. Recently, the effect of high molecular weight polymer on the low-flow limit of slot coating was examined by visualization experiments and theoretical analysis using an algebraic non-Newtonian model that takes into account the extensional thickening behavior of polymer solutions. Although Generalized Newtonian Models of this class may capture the different ways that dilute polymer molecules behave in extension- and shear-dominated flow zones and the reported predictions display the same trends that are observed experimentally, algebraic models cannot represent viscoelastic stresses. In the present work, the low-flow limit of slot coating of mildly viscoelastic liquids is examined by solving the conservation equations for two-dimensional flow, coupled with either of two differential viscoelastic models that describe the mechanical behavior of dilute polymer solutions (namely the Oldroyd-B and FENE-CR models). The results show how the different theological properties affect the flow and the critical conditions at the onset of the low-flow limit. (c) 2006 Elsevier B.V. All rights reserved.