The invention relates to compositions which contain at least one isocyanate-containing polyurethane polymer P, which is produced from at least one polyisocyanate and at least one polyol, in addition to at least one aldimine-containing compound of formula (I). The compositions are stable during storage and harden quickly under the influence of moisture, are non-porous and do no not separate rich substances. Said compositions, the hardened compositions, and the resulting separated products are odor-less. The compositions can be used as an adhesive, sealant or coating which exhibit good mechanical properties and adhesion.