Moisture-curable organosilicon compositions which are storable in the absence of water, and crosslinkable on admission of water at room temperature to give elastomers, are based on organosilicon compositions containing: (A) compounds of the formula A-[(CR.sup.1.sub.2).sub.b--SiR.sub.a(OR.sup.2).sub.3-a].sub.x (I), (B) an organosilicon compound having basic nitrogen and (C) compounds of the formula R.sup.3--NH--C(.dbd.O)--C(.dbd.O)--NH--R.sup.3, and (II) optionally, further additives.