[en] The results of the studies of the decay of thallium isotopes establish the coexistence and crossing of two bands in the mercury isotopes. The two bands are built on states of different deformation. The band built upon the ground state has an associated small negative β value (oblate shape) while the second band has a large positive β value (prolate shape). The band heads for the deformed bands in the ^184186188Hg isotopes are established as 0⁺ levels at 375.2, 523.8, and 824.5 keV respectively. A comparison between the experimental results and the predictions of calculations based upon the coexistence of two different nuclear deformations has been made. The presence of two different deformations as described by two minima in the nuclear potential energy curve is termed ''shape coexistence.'' The good agreement of the calculations with the experimental results adds further support to the coexistence interpretation. The coexistence and crossing of two bands of different deformation explains the unusual behavior of the yrast level spacing that is referred to as 'backbending' when discussing moment of inertia versus rotational frequency plots based on the yrast levels. The studies of the ¹⁸⁶¹⁸⁸Pt levels have established the lower members of the ground state band and of a rotation-alignment band. The experimental results confirm the rotation-alignment explanation of backbending in the platinum cases discussed. (Auth.)