The stability of a bicomponent two-layer blown film coextrusion process has been studied using a simple model in which the two layers consist of a Newtonian and an upper-convected Maxwell fluid (UCM), respectively. These two fluids are chosen to investigate the relative influence of viscous and viscoelastic forces on the stability of the two-layer biaxial extension flow. The results of the linear stability analysis indicate that a critical value of the film thickness exists below which the flow becomes unstable. The critical film thickness decreases with increasing the blow-up ratio (BUR). While a Newtonian single-layer flow exhibits an upper unstable region where the flow is unstable when the BUR is greater than a certain critical value, the presence of a thin viscoelastic layer removes the upper unstable region. It also enhances the flow stability by broadening the range of operating conditions for stable operation. Although the present model is rather simple, many of the predictions appear to be in reasonable agreement with experimental observations qualitatively. (C) 2000 Elsevier Science B.V. All rights reserved.