The ground electronic state of argon hydride has a repulsive potential apart from a long-range van der Waals minimum, but the Rydberg excited states have bound potentials similar to those of the ion ArH+. These states can be described approximately in terms of united-atom quantum numbers nl. We report here rotational analyses of the bands 5p-->5s, 5p-->6s, and 6p-->5s of ArD, which help to further characterize the np Rydberg series. In ArH the bands 5p-->5s and 6p-->5s have broad lines because of predissociation in the lower state, and 5p-->6s is difficult to analyze without further information. The present data are fitted with a Hund’s case (d) effective Hamiltonian. In previous work the 4p state was found to have a very small sigma-pi splitting, but this does not hold for the higher np states, and is probably due to an accidental cancellation between electrostatic and polarizability contributions. On the other hand, the spin-orbit coupling decreases monotonically with n. Features of the rotational levels are discussed in terms of the high-J limiting quantum numbers l(J)=N-R and s(J)=J-N, where R=N+, in particular the effect of spin-orbit coupling on the levels with (l(J),s(J)) =(-1,1/2) and (0,-1/2), which produces a tendency to Hund’s case e behavior in 4p, and a sharp avoided crossing in 6p. The corresponding avoided crossing in 5p would occur beyond the present range of observed J values.