Co-continuous morphologies are found over a wide composition range (30-80 vol%) in blends of a polystyrene thermoplastic and a poly(ether-ester) thermoplastic elastomer when they are blended below the block copolymer＇s order-disorder transition (ODT). This range decreases with increasing processing temperature and becomes limited when both polymers show pseudo-plastic behaviour. Annealing of the co-continuous blends below the ODT hardly influences the phase sizes and composition range, but when annealing takes place at higher temperatures the blends show an increase of their phase domains and the composition range decreases. The condition for the formation of co-continuous morphologies, especially at low volume fractions, is the existence of stable interconnected elongated structures, that do not show breakup or retraction. Breakup and retraction experiments on poly(ether-ester) fibres embedded in a polystyrene matrix make clear that these mechanisms can be severely limited or even stopped and therefore the condition for the existence of co-continuous morphologies is fulfilled.