The pure rotational spectra of ZrO and ZrS have been recorded using cavity Fourier transform microwave spectroscopy in the frequency range 9-26 GHz. The molecules were generated by laser ablation of a solid Zr rod in the presence of 0.05% of O-2 or H2S, respectively, in either argon or neon. Rotational spectra of five previously unobserved isotopomers of ZrO in the X(1)Sigma(+) state have been measured. Spectra for all five (ZrS)-S-32 isotopomers and for the (ZrS)-Zr-90-S-34 isotopomer in natural abundance have also been measured; this is the first report of pure rotational transitions for ZrS. Transitions in several excited vibrational states were also measured for the most abundant isotopomers of both species. Atomic mass-dependent Born-Oppenheimer breakdown correction terms were determined by fitting the data obtained for each molecule to a Dunham-like expression. Values for the equilibrium bond lengths of the two species were also calculated from the results of these fits. For both the (ZrS)-Zr-91-S-32 and (ZrO)-Zr-91-O-16 isotopomers, nuclear hyperfine structure due to the zirconium nucleus was observed and values for eQ(q0) (Zr-91) and C-I (Zr-91) have been determined. A rotational transition in the low lying a (3)Delta state of ZrS has also been observed.