The fine structure constant (electron spin-spin coupling) and the hyperfine structure parameters (electron-nuclear spin coupling, including spin-rotation and electron-nuclear quadrupole coupling) in the low-lying triplet states b (3)Sigma(u)(+), a (3)Sigma(g)(+) and e (3)Sigma(u)(+) of molecular hydrogen and deuterium are calculated using a recently developed technique with full configu-ration interaction and multiconfiguration self-consistent field wave functions. The second-order spin-orbit coupling contribution to the (3)Sigma(+) states splitting is negligible, and the calculations therefore provide a good estimate of the zero-field splitting based only on the electron spin-spin coupling values. For the bound state a (3)Sigma(g)(+) negligible zero-field splitting is found, in qualitative agreement with the e-a spectrum. The zero-field splitting parameter is considerable for the repulsive b (3)Sigma(u)(+) state (similar or equal to1 cm(-1) ) and of intermediate size for the bound e (3)Sigma(u)(+) state. The isotropic hyperfine coupling constant is very large not only for the valence b (3)Sigma(u)(+) state (1580 MHz) but also for the Rydberg a and e triplet states (similar or equal to1400 MHz). The quadrupole coupling constants for the deuterium isotopes are negligible (0.04-0.07 MHz) for all studied triplet states. The electric dipole activity of the spin sublevels in the triplet-singlet transitions to the ground state is estimated by means of the quadratic response technique.