Stable co-continuous morphologies are found over a wide composition range in blends of styrene/(ethylene-butylene) based block copolymers (SEBS) and polypropylene (PP) when they are processed below the block copolymer's order-disorder transition (ODT), i.e. when the block copolymers are microphase-separated. Blending at higher temperatures, i.e. when the block copolymer shows a single-phase melt, also leads to a reasonably wide composition range of co-continuity but when annealing takes place at these temperatures the blends show an increase in their phase domains and the composition range decreases significantly. Annealing of the co-continuous PP/SEBS blends when the block copolymers are microphase-separated hardly influences the phase sizes and composition range. Blending the same block copolymers with polymethyl methacrylate or polyoxymethylene, leading to blends with much higher interfacial tensions, results in a much smaller composition range of co-continuous morphologies than was found in the PP/SEBS blends, whatever the processing temperature be. It is demonstrated that breakup and retraction can be severely limited or even stopped at lower blending temperatures, therefore fulfilling the condition for stability of co-continuous morphologies. The (non-)breakup or (non-)retraction behaviour of elongated structures strongly depends on a complex combination of parameters, including phase size, yield stress and interfacial tension. Therefore the formation of stable co-continuous morphologies also strongly depends on these parameters.