  The reanimation of the investigations dedicated to 0^{+} states energies and
E0 transitions between them is provoked by new and more precise experimental
techniques that not only made revision of the previous data but also gave a
possibility to obtain a great amount of new 0^{+} states energies and
conversion electrons data. We suggest one phenomenological model for estimation
of the E0 transition nuclear matrix elements. Recently theoretical calculations
[1] predicted existence of a 0^{+} state with energy 0.68 MeV in ^{160}Dy
nucleus. Powerful enough arguments in favor of existence of 681.3 keV state in
^{160}Dy nucleus are presented.
