At least partially hydrolyzed chlorosulfonated polyolefin elastomers containing 0.5-10 weight percent chlorine and 0.25 to 5 weight percent sulfur are prepared from low density polyethylene or from linear ethylene/alpha-olefin copolymer base resins having a ratio of weight average molecular weight (Mw) to number average molecular weight (Mn) less than 3.5.