Electronic state-dependent Ar.NH(X,a,b) potential surfaces from ab initio calcns. were combined with a classical model of a doped rare-gas matrix to calc. electronic matrix shifts and local-mode frequencies which compare favorably with spectroscopic observations. NH/ND substitutes 1 Ar atom in sites of Oh and D3h symmetry which occur with equal probability over a wide range of exptl. conditions, while interstitial trapping and impurity effects could be excluded. The previously reported site-dependent rotational-electronic (rotronic) splitting in the a 1D state of NH is insensitive to deuteration. The partial lifting of the 10-fold degeneracy in the lowest rotronic level of the a 1D state could be modeled for both site symmetries by evaluating the effect of the rare-gas cage in 1st-order perturbation theory. The NH(a).Arn interaction is constructed from the av. of a recently published pair of ab initio NH(a1A').Ar and NH(a1A).Ar potential surfaces. Electronic splitting is introduced via a difference potential surface of NH-(a).Ar12 which was obtained by quantum mech. methods, as described in detail in an accompanying paper. The perturbation gives rise to rotronic splittings which differ in cages of Oh and D3h symmetry. The selection rules governing transitions from the electronic ground state to the sublevels of NH a1D in cages of Oh and D3h symmetry are consistent with the obsd. spectra.