To obtain a polyurethane sealant or adhesive which is based on a satd. polyhydroxylated polybutadiene and has improved tack and peel strength.

A polyurethane compsn. is provided which contains a polyisocyanate having a functionality of 2.2-10 and a substantially satd. polyhydroxylated polydiene having a hydroxyl equivalent of 500-20,000 in an equivalent ratio (NCO/OH) of (0.3:1)-(0.7:1) or a mixture comprising 85-25 wt.% substantially satd. monohydroxylated polydiene having a hydroxyl equivalent of 500-20,000 with 15-75 wt.% substantially satd. polyhydroxylated polydiene having a hydroxyl equivalent of 500-20,000 in an equivalent ratio (NCO/OH) of (0.9:1)-(1.1:1).