The nuclear hyperfine structure of OD and Ar . OD in their A (2) Sigma(+) electronic states has been studied by quantum beat spectroscopy. The very cold transient species were produced in a supersonic expansion using a pulsed discharge nozzle. Coherent excitation of hyperfine (hf) states, arising from one fine structure (OD) or rotational (Ar . OD) level, created quantum beats on the fluorescence decay. The beat frequencies, which correspond to energy separations between hf levels, could be measured to +/-75 kHz. The splitting of the hf levels into their Zeeman components was investigated in a weak magnetic field. A fit of the zero field and Zeeman data yielded the relevant constants for the nuclear magnetic and electric quadrupole hyperfine interactions as well as the pertinent g-factors in each species. In the case of OD, the hf parameters agree well with those reported previously but are more accurately defined. For Ar . OD the previously unknown hyperfine and spin-rotation parameters of the A (2) Sigma(+) State were determined. A comparison of the hf parameters in the two systems allowed assessment of the effect of van der Waals complex formation on the electron distribution. Thus complexation is found to reduce the unpaired electron density on the deuteron by 7% which is indicative of significant chemical bonding between the Ar atom and the OD moiety in the A (2) Sigma(+) state of Ar . OD. For both systems, the g-factors g(s) and g(l) obtained suggest an admixture of other, possibly quartet, electronic states into the A (2) Sigma(+) state.