[en] Using a coherent pulsed NMR spectrometer operating at 5.9 MHz, measurements have been made of the free induction decay and of the solid echo in hcp solid D₂. From these data, and using Fourier transform techniques, the NMR line shapes and longitudinal relaxation times have been found for both o-D₂ (angular momentum J = 0 and spin I = 2) and p-D₂ (with J = 1 and I = 1) separately. The concentration and temperature extended over the ranges 0.05 ≤ X(J = 1) ≤ 0.56 and 0.04 < T < 3 K, respectively. For both o-D₂ and p-D₂, the second moment of the NMR line shape rises smoothly as the temperature decreases, while the relaxation times pass through a minimum. No evidence of a thermal hysteresis could be found in the line shape or relaxation times. The orientational ordering increases continuously as the temperature decreases and the results lead to the conclusion that there is no evidence for a well-defined transition into a phase that has the characteristics of a glassy state, at least above 0.05 K. calculations of the rms order parameter o for p-D₂ as a function of X and T are presented and the results compared with those for solid H₂. Above ≅ 0.5 K, the agreement is very good, while below ≅ 0.3 K, o(H₂)> σ (D₂). The orientational polarization of the J = 0 molecules in D₂ by the surrounding J = 1 molecules is measured from the ratio of the lineshape second moments and is found to be in order-of-magnitude agreement with the predictions by A. B. Harris in the high-temperature limit. An analysis and correlation of the various measured relaxation times via energy diffusion models is presented. From the spin-lattice relaxation times of the J = 1 molecules, the orientational fluctuation rates are estimated for various concentrations as a function of T and compared with the results from H₂