Pure rotational spectra of Ne-SH and Kr-SH have been studied by Fourier transform microwave spectroscopy. R-branch transitions in the lower-spin component (Omega=3/2) corresponding to a linear (2)Pi(i) radical were observed for J"=1.5-4.5 in the region 11-25 GHz for Ne-SH and for J"=1.5-6.5 in the region 5-20 GHz for Kr-SH, respectively, with parity doublings and hyperfine splittings associated with the H nucleus. Although the spectral pattern of Kr-SH is relatively regular, that of Ne-SH is irregular with the J dependence of the parity doublings quite different from other Rg-SH or Ar-OH complexes. Two-dimensional intermolecular potential energy surfaces (IPSs) for both of the species have been determined from the least-squares fittings of the observed rotational transitions utilizing results of high-level ab initio calculations. These IPSs reproduce the observed transition frequencies within the experimental error and provide accurate knowledge on the intermolecular interaction and internal dynamics. Systematic comparisons of Rg-SH complexes have clarified various features of this series of complexes. (C) 2004 American Institute of Physics.