We report observations and analyses of bands in the spectra of the ArH and ArD molecules due to emission from the 4f Rydberg complexes. For ArD, the observed bands are 4f --> 5s and 4f --> 3dlambda for all three components lambda = 0, 1, and 2 of the 3d state. These give direct information on all 14 spin-orbit components of the 4f complex. For ArH, the data is more limited because the levels of the 5s state are broadened by predissociation, and only the lambda = 2 component of the 4f --> 3dlambda transitions is seen clearly, although a number of lines could be assigned to the 4f --> 3dpi band, which is strongly overlapped by the 6s --> 4p band. The 4f complexes of both isotopes are good example of Hund's case (d) coupling. The 4f orbitals are essentially non-core-penetrating, so that spin-orbit coupling is negligible for them, and the zero-rotation splitting agrees well with calculations from the ab initio quadrupole moment and anisotropic polarizability of the core. The orbit-rotation coupling parameter xi4f gives a value of the core electric dipole moment that is in reasonable agreement with ab initio and previous experimental values. A summary of the presently known states of ArH and ArD is presented. Copyright 1998 Academic Press.