Polymers of a conjugated diene, an unsaturated nitrile and an .alpha.,.beta.-unsaturated carboxylic acid are selectively hydrogenated to reduce carbon-carbon double bonds, without also reducing carboxyl groups and nitrile groups, using a rhodium-containing compound as catalyst. The hydrogenated polymers are novel and display excellent adhesive properties at both room temperature and high temperature, excellent hot tear strength, and excellent abrasion resistance.