The present invention relates to the use of zinc complexes of natural amino acids, especially L-arginine, L-lysine, L-ornithine, and other natural amino acids, in a molar ratio of about 1:2 (metal:amino acid), and formulations thereof. These pharmaceutical compositions offer better tolerated and faster acting regimens than common zinc salts (i.e., acetate, sulfate, etc.) for long term maintenance therapy of diseases caused by abnormal elevated copper levels, such as in Wilsons disease, inflammatory and fibrotic diseases and Alzheimers disease.