Nuclear quadrupole coupling constants for KrH+, XeH+ and XeD+ are combined with Douglas-Kroll (DK) CCSD(T) calculations to obtain the nuclear quadrupole moments of +259(1) and -114(1) millibarn (1 mb = 10(-31) m(2) for Kr-83 and Xe-131, respectively. For the radioactive isotopes Kr-81 and Kr-85, the available atomic isotopic ratios give a Q of +644(4) and +443(3) mb, respectively. For the Kr-83 9.4 keV I = 7/2 Mossbauer state, Q(Kr-83*) of 507(3) mb is derived from our data. For the Xe-129 40 keV I = 3/2 Mossbauer state, Q(Xe-129*) is -393(10) mb.