Moisture-curing compositions include at least one silane-functional polymer P with at least two terminal groups of formula (I) and at least one reaction product R which is produced from at least one aminosilane AS with at least one primary amino group and at least one silane group-free alkene M which is capable of entering in 1,4 addition reactions with primary amino groups. The compositions have improved adhesive properties and are especially suitable for use as adhesives, sealing materials or coatings, especially as elastic adhesive or sealing materials.