A multi-layered pipe of arbitrary length and cross-section is produced by co-extrusion of a lower polyolefin (C.sub.2 C.sub.4) outer body over the exterior surface of a tubular core of randomly, partially randomly, or blocky chlorinated lower polyolefin, the core having a wall thickness, measured in the radial direction, in the range from about 0.025 mm to 5 mm. The tubular core is coextensive with essentially the entire length of the pipe. The tubular core comprises a major proportion by weight of the randomly chlorinated polyolefin (r-CPO), or, partially randomly chlorinated polyolefin (pr-CPO), or, a blocky chlorinated polyolefin (b-CPO), any of which may be blended with a minor proportion by weight of a blending ingredient. The r-CPO, pr-CPO or b-CPO, or a blend thereof, each has an extrusion temperature in the same range as that for the corresponding non-halogenated polyolefin, namely in the range from about 150.degree. C. to 250.degree. C.