We report and rotationally analyze new spectra of the ArH and ArD molecules corresponding to the 0-0 vibrational bands of electronic transitions from the nd and ns states to the 4p Rydberg complex, in united atom notation. In ArD, our observation of the 3ddelta state, along with previous observations of the 3dpi and 3dsigma states, demonstrates that the components of the 3d state are widely separated and can be treated as Hund's case (b) states, unlike the components of the np and 4f states, which form closely coupled case (d) Rydberg complexes. The band 4dsigma --> 4p has also been assigned. The 4dpi component is known from previous work of Lipson, but as yet the 4ddelta component is unknown. Emission from the 6s and 8s states is also analyzed. From the intensities in the rotational structure, there is evidence that the 6s state interacts with the 3dsigma state. In ArH, we analyze the 0-0 bands of the 3dpi --> 4p, 3ddelta --> 4p, 4dsigma --> 4p, and 6s --> 4p transitions. Unlike the rotational levels of the 5s state, which are heavily broadened by predissociation, the 4p levels of ArH are sharp, so we can perform a more accurate and detailed analysis for this isotope than was possible previously. Qualitative features of the ArH spectra essentially mirror those of ArD, except that emission from the 3dsigma state was not identified, possibly due to a perturbation particular to this isotope. Copyright 1998 Academic Press.