What is the nature of Kπ = 0+ bands in deformed nuclei?

New data is presented on Kπ = 0+ bands in 156,158Gd and 178Hf. Each of these nuclei exhibit a different aspect of the nature of Kπ = 0+ bands in deformed nuclei. In 156Gd, there is evidence of a Kπ = 0+ band with significant two-phonon γγ component whereas in 178Hf results are shown for a Kπ = 0+ band whose members exhibit two-phonon ββ character. New (p,t) reaction results point to the existence of thirteen excited 0+ states in 158Gd below an excitation energy of 3.1 MeV. All the results combine to provide a challenge to our present understanding of the nature of these excitations