Preparing a polyurethane with polyurethane-polyether and polyurethane-polyester blocks with at least 2 polyurethane-polyester end blocks joined to an alkoxysilane end group, by reaction of a polyether polyol (A) with a stoichiometric excess of an aliphatic diisocyanate (B), then reaction of the polyurethane formed with a stoichiometric excess of a polyester polyol, then reaction of the polyurethane formed with a stoichiometric amount of an isocyanatosilane (D); polyurethane formed by said method; corresponding adhesive composition, further comprising a crosslinking catalyst method of assembly of 2 substrates employing the composition.