The existence of optimal cooling conditions with respect to process stability has been experimentally found in film blowing, in a sharp contrast to other extensional deformation processes such as fiber spinning and film casting where maximum, not optimal, cooling always unequivocally enhances process stability. The same simulation model of film blowing of Hyun et al. [J.C. Hyun, H. Kim, J.S. Lee, H.-S. Song, H.W. Jung, Transient solutions of the dynamics in film blowing processes, J. Non-Newtonian Fluid Mech., 121 (2004) 157-162] proven quite accurate in portraying the transient dynamic behavior of the film blowing as compared with experimental data, has been used in this study to carry out. a linear stability analysis, which then clearly confirms the experimentally found optimal cooling conditions. These optimal cooling conditions in film blowing stemming from the multiplicity of steady states of the process thus make the strategies for stabilization and optimization of the process quite a challenging task in both industry and academia because of their common relevance to the important process productivity issue. (c) 2006 Elsevier B.V. All rights reserved.