Method for preparing a cross-linkable composition

A process for preparing a crosslinkable composition comprising at least one alkoxysilane-terminated silyl polymer P, and at least one catalytic system B, said process comprising the following steps:

• a) preparing an alkoxysilane-terminated silyl polymer P comprising:
• a-1) a polyaddition reaction between a composition of polyol(s) and a composition of polyisocyanate(s), in the presence of a catalyst A selected from the group consisting of carboxylates based on bismuth and zinc or carboxylates based on zinc, in order to prepare an NCO-terminated polymer;
• a-2) a reaction of the NCO-terminated polymer obtained in step a-1) with an aminosilane compound having at least one function that is reactive with the —NCO function of the NCO-terminated polymer;
• and
• b) bringing the silyl polymer P obtained in step a) into contact with a catalytic crosslinking system B, which is a mixture of zinc-based carboxylate(s) and cyclic amidine,
• said process being carried out in the absence of a tin-based catalyst.