The morphologies of blends of polyethylene (PE) with a range of copolymers with different basic structure (diblock, triblock, starblock or statistical) have been compared in order to assess the relative importance and interrelation of rheological and molecular parameters. The development of well defined dispersed phases in extruded-blown PE films results from two successive steps. The first is the dispersion step, dominated by shear force fields and shear viscosity in the extruder barrel and die. The second step involves drawing of the melt and freezing of the structures. If the dispersed phase is characterized by a high value of the shear viscosity ratio η d η m and hence by a low deformability, elongation can be performed in neither step. This was observed for diblock styrene-butadiene (SB) in a low viscosity PE matrix, for SBS r2 and for StatSB which all give spheres or ellipsoids. The dimension of the spheres is governed by the viscosity of the matrix and by the value of η d η m according to the Wu equation. If the dispersed phase is highly deformable ( η d η m < 1 ), it is elongated in one or two dimensions at the exit of the die. For a Newtonian melt, these structures break during the elongation time preceding freezing of the structures if the breaking time given by Tomotika's theory is shorter than the elongation time. Broken filaments have indeed been observed for SBS at 240°C and also for styrene-isoprene-styrene (SIS) at 270°C. For a non-Newtonian dispersed phase, stabilization of the structures occurs by different mechanisms involving the elastic contribution of the elongational viscosity. It is related to entanglements and increases with molecular weight. Yielding or tension thickening behaviour can be involved. This is illustrated by the formation of co-continuous elongated structures when the high-molecular-weight diblock SB and triblock SIS are blended with PE, respectively at 240 and 220°C. Two starblock copolymers, SBS r1 and SBS r3, although non-Newtonian and characterized by a rather low value of η d η m , do not give continuous structures. This is attributed to the low molecular weight of the branches which does not allow the formation of a sufficient number of entanglements.