We present an experimental study of H and D atoms trapped in a solid D 2 matrix. The samples were prepared by quench condensing gaseous nD 2 with small (0.15 %) admixture of molecular nH 2 on a substrate at 1.3-4.2 K. An EPR observation revealed two types of H and D atoms: with narrow-and broad-line spectra. In order to elucidate the origin of the centers we performed an analysis that included comparing the matrix shifts of the hyperfine structure constants, considering the saturation and spin-relaxation times, estimation of the superhyperfine broadening, and evaluation of an effect which the tunneling isotope exchange reaction has on the H and D atoms relative EPR intensities. As a result, the broad-line H and D spectra were attributed to atoms at the substitutional positions in the regular D 2 lattice, while the narrow-line spectra were due to atoms trapped at the one-dimensional structure imperfections (like dislocations). These trapped atoms are capable of moving quickly along the defects with a diffusion coefficient D ≈ 4 × 10 −6 cm 2 /s. The results were compared to earlier observations which allowed us to build a suggestion about the nature of previously found atomic centers in D 2 not explained in the literature.