It is shown that the Mallmann's energy correlations, introduced a long time ago for the ground state bands of the even–even nuclei are, in fact, universal. Various bands in all collective nuclei (even–even, odd–even, and odd–odd) obey the same systematics. This unique, universal behaviour indicates the same spin dependence of the energy of the levels in all bands in all collective nuclei. Based on a second-order anharmonic vibrator description, parameter-free recurrence relations between energy ratios are deduced. These relations can be used to predict levels of higher spins in various bands.

PACS numbers: 21.10.–k, 21.10.Re