[en] 'Identical bands' (i.e. those with surprisingly similar moments of inertia) have been found through several analyses of known bands in normally deformed nuclei. The bands in odd-proton nuclei (A = 150 ∼ 190) and A-1 even-even adjacent nuclei are analyzed with stringent criteria. The 'identical bands' are found to be associated with up sloping particle states. Therefore the cause of occurring 'identical bands' may be a cancellation of effects on the moment of inertia between pairing and deformation reduction. The related challenges to the traditional nuclear theory are described as well