Embodiments of the invention provide for methods of producing a composition comprising a crosslinkable silane-terminated polymer having at least one crosslinkable silyl group in each molecule. The method comprises providing a polymer having at least one unsaturated group and at least one alcoholic hydroxyl group in each molecule, adding to the polymer a compound having a hydrogen-silicon bond and a crosslinkable silyl group in each molecule and a hydrosilylation catalyst to thereby carry out a hydrosilylation reaction to form a composition comprising hydrosilylated polyoxyalkylene polymers, reacting the hydrosilylated polyoxyalkylene polymers with at least one isocyanate in the presence of a first tin-free catalyst to form an isocyanate reacted hydrosilylated polymer, and optionally reacting the isocyanate reacted hydrosilylated polymer with a polyol having a nominal functionality of at least 2 to form a polyol reacted crosslinkable silane-terminated polymer.