The millimeter and submillimeter-wave molecular-beam spectrum of the perdeuterated ammonia dimer (ND3)(2) has been measured between approximately 50 and 400 GHz using an electric-resonance optothermal spectrometer (EROS). As in the case of the (NH3)(2), the spectrum is complicated by the threefold internal rotation of the ND3 subunits, the interchange tunneling of the two subunits, and the inversion of the subunits through their respective centers of masses. These tunneling motions split the rigid-molecule energy levels into 22 components, which all have nonzero statistical weights in the case of the deuterated dimer. Transitions have been assigned for rotation-tunneling states correlating to A-A (ortho-ortho) combinations of the ND3 monomer states, where A designates the rovibronic symmetries of the ND3 subunits. One K=1<--1, one K=1<--0, one K=0<--1, and two K=0<--0 progressions have been assigned. The data have been fit to 0.28 MHz using linear molecule-type energy-level expressions to determine rotational constants, band origins, l/K-type double constants, and centrifugal distortion constants. The two K=0<--0 subbands, with origins near 264 GHz, are split by 64 MHz due to monomer inversion, as observed previously in the NH3 dimer. The 264 GHz, K=0 splitting arises predominantly from monomer interchange tunneling and is nearly a factor of 2 less than the 483 GHz value for the NH3 dimer. The separation is also approximately 25% smaller than predicted by Olthof et al. [E. H. T. Olthof, A. van der Avoird, and P. E. S. Wormer, J. Chem. Phys. 101, 8430 (1994)] from dynamical calculations on a model potential energy surface adjusted to fit the observed far-infrared rotation-tunneling spectrum of the NH3 dimer.