One-component, moisture curing compositions which exhibit rapid curing, even with exceptionally low levels of catalyst or with no catalyst at all, can be formulated from alkoxysilane-terminated polymers having alkoxysilane groups bonded to an electronegative, free electron-pair-containing heteroatom via a methylene linking group. Polymer blends containing the alkoxysilane-terminated polymers exhibit rapid cure, even at room temperature, and allow the use of nitrogen containing components such as adhesion promoters.