A curable polymer composition comprising:(A) 100 parts by weight of an oxyalkylene base polymer having at least one silicon-containing group to the silicon atom of which a hydroxy group and/or a hydrolyzable group is bonded and which is cross linkable through formation of a siloxane bond,(B) 0.1 to 20 parts by weight of at least one compound selected from the group consisting of a compound having one silanol group in the molecule and a compound which, when reacted with moisture, generates a compound having one silanol group in the molecule,(C) 0.1 to 20 parts by weight of a compound having a silicon-containing group to the silicon atom of which two hydrolyzable groups are bonded and an amino group, and(D) 0.01 to 5 parts by weight of a compound having a silicon-containing group to the silicon atom of which three hydrolyzable groups are bonded and an amino group, which composition provides a cured material having low modulus, group bond strength and improved weather resistance of bond strength.