A viscous block copolymer of the formula(A--B--A).sub.n --Y.sub.r --(A.sub.q --B).sub.mwherein Y is a coupling agent or coupling monomers, andwherein A and B are polymer blocks which may be homopolymer blocks of conjugated diolefin monomers, copolymer blocks of conjugated diolefin monomer or copolymer blocks of conjugated diolefin monomers and monoalkenyl aromatic hydrocarbon monomers, andwherein the A blocks have a higher number of aliphatic double bonds between a tertiary carbon atom and either a primary or secondary carbon atom per unit of block mass than do the B blocks, andwherein the A blocks have a molecular weight from about 100 to about 3000 and the B blocks have a molecular weight from about 1000 to about 15,000, andwherein p and q are 0 or 1 and n>0, r is 0 or 1, m.gtoreq.0 and n+m ranges from 1 to 100.This block copolymer is preferably partially hydrogenated, epoxidized and crosslinked through at least some of the epoxy functionality to form an adhesive, coating or sealant composition.