Long lengths of a heat-shrinkable sleeve for use in splicing electrical cables are manufactured by providing an elongated impermeable core, extruding an elongated sleeve around and in contact with the core, and effecting an initial expansion of a portion of the sleeve to a larger diameter in an expansion zone (40) so that the sleeve separates and leaves a space between the sleeve and core. A fluid is introduced into the space under pressure via a fitting (62) at the downstream end of the sleeve. To begin the process, a permeable core (26) is used, and the sleeve is extruded around and in contact with the permeable core. A fluid is introduced under pressure from a fitting (52) upstream or downstream of the expansion zone through the permeable core to the inside the sleeve in the expansion zone, and the leading end of tt impermeable core is welded at (50) to the trailing end of th permeable core at a location upstream of the expansic zone. To form the sleeve, an inner compound and a thin lay of outer compound are applied in a crosshead (38a), and balance of the outer compound is applied around the sleev in a second crosshead (38b). Liquid nitrogen cools an stabilizes the inchoate sleeve at (110).