The high resolution laser-induced fluorescence spectra of the Kr.OH van der Waals complex and its deuterated analog are reported. The rotational analysis provides information about the observed fine, hyperfine, spin-rotation, and parity interactions in these two complexes. The molecular parameters allow a direct comparison with previously reported results on the analogous Kr.SH/D complexes. Additionally, lower resolution scans have revealed vibronic bands that have not been reported in the previous work of Fei, Zheng, and Heaven [J. Chem. Phys. 97, 1655 (1992)],while high resolution results of the Kr-86.OH/D, Kr-84.OH/D, and Kr-82.OH/D isomers confirmed the previous vibrational quantum number assignment. The results of the high resolution analysis are used in conjunction with measured vibrational intervals to develop an empirical potential energy surface for Kr.OH/D. This is compared to the recently reported potentials by Korambath et al. [J. Chem. Phys. 107, 3460 (1997)] for the other R.SH/D (R = Ar, Kr) complexes.