Among rare gases, xenon features an unusually broad nuclear magnetic resonance (NMR) chemical shift range in its compounds and as a non-bonded Xe atom introduced into different environments. In this work we show that ¹²⁹Xe NMR chemical shifts in the recently prepared, matrix-isolated xenon compounds appear in new, so far unexplored ¹²⁹Xe chemical shift ranges. State-of-the-art theoretical predictions of NMR chemical shifts in compounds of general formula HXeY (Y = H, F, Cl, Br, I, –CN, –NC, –CCH, –CCCCH, –CCCN, –CCXeH, –OXeH, –OH, –SH) as well as in the recently prepared ClXeCN and ClXeNC species are reported. The bonding situation of Xe in the studied compounds is rather different from the previously characterized cases as Xe appears in the electronic state corresponding to a situation with a low formal oxidation state, between I and II in these compounds. Accordingly, the predicted ¹²⁹Xe chemical shifts occur in new NMR ranges for this nucleus: ca. 500–1000 ppm (wrt Xe gas) for HXeY species and ca. 1100–1600 ppm for ClXeCN and ClXeNC. These new ranges fall between those corresponding to the weakly-bonded Xe0 atom in guest–host systems (δ < 300 ppm) and in the hitherto characterized Xe molecules (δ > 2000 ppm). The importance of relativistic effects is discussed. Relativistic effects only slightly modulate the ¹²⁹Xe chemical shift that is obtained already at the nonrelativistic CCSD(T) level. In contrast, spin–orbit-induced shielding effects on the 1H chemical shifts of the H1 atom directly bonded to the Xe center largely overwhelm the nonrelativistic deshielding effects. This leads to an overall negative 1H chemical shift in the range between −5 and −25 ppm (wrt CH4). Thus, the relativistic effects induced by the heavy Xe atom appear considerably more important for the chemical shift of the neighbouring, light hydrogen atom than that of the Xe nucleus itself. The predicted NMR parameters facilitate an unambiguous experimental identification of these novel compounds.