Based on density functional calculations, we have found that axial compression can induce structural transitions between Au(n,n) and Au(2n,n) nanotubes. The corresponding energy barriers increase with n. Although Au(2n,n) nanotubes are energitically more stable, the energy difference between Au(n,n) and Au(2n,n) decreases with n. The structural transitions are believed to be unique in those nanotubes with metallic bonds, while nanotubes with covalent bonds, such as carbon nanotubes, will not have these features.