Isolated, monoclonal, human, anti-.beta.-amyloid antibodies are provided which bind to dimeric forms of Ab with higher affinity than to monomeric forms of Ab and when bound to an A.beta. polypeptide comprising A.beta.(21-37) shield A.beta.(21-37) from proteolytic digestion. The antibodies were shown to inhibit fibril formation and reduce plaque size in vivo and to not bind brain vessel walls. Accordingly, the antibodies are useful in human and veterinary medicine for the treatment and prophylaxis of Alzheimer's disease and other neurodementing diseases. Methods of detecting or measuring the progression of a neurodementing disease also are provided.