The invention relates to methods of treating a subject having Alzheimers Disease, comprising the step of administering an antibody molecule which is targeted to β amyloid peptide or to fragment thereof. In another embodiment the invention relates to methods of treating a disease or a disorder, characterized by amyloid beta deposition. In another embodiment, the invention relates to an antibody molecule, which is free end-specific for the N-terminus or the C-terminus of an amyloid β peptide and to a pharmaceutical composition thereof. In another embodiment, the invention relates to an antibody molecule, which is targeted to the free C or N-terminus of a N- and/or C-terminus truncated amyloid β peptide fragment.