Nonequilibrium phase transformations in D2O ices, including the solid-state amorphization of ice 1h (1h-hda) and the heating-induced transition cascade hda-lda-1c-1h from high-density amorphous (hda) ice to low-density amorphous (lda) ice followed by crystallization in cubic ice 1c and phase transition to ordinary hexagonal ice 1h, were studied using an ultrasonic technique. It has been shown that, as in H2O ice, the softening of a crystal lattice or an amorphous network precedes nonequilibrium transformations. However, noticeable isotopic differences in the behavior of the elastic properties of H2O and D2O, in particular, their 1h and hda modifications, call for a more detailed study of the structural features of these H2O and D2O phases.