The invention relates to hot-melt adhesive (HMA) compositions which are provided in the form of a polymer containing free isocyanate functional groups, the said polymer resulting from the reaction of a polyisocyanate (A), of a polydienopolyol (B) and of a copolymer (C) of ethylene containing hydroxyl functional groups. They have a low viscosity and can thus be employed from 110° C. They can be crosslinked with atmospheric moisture.