The pure rotational spectra of 27 isotopic species of SnSe and SnTe have been measured in the frequency range of 5-24 GHz using a Fabry-Perot-type resonator pulsed-jet Fourier-transform microwave spectrometer. Gaseous samples of both chalcogenides were prepared by laser ablation of suitable target rods and were stabilized in supersonic jets of Ar. Global multi-isotopolog analyses of all available high-resolution data produced spectroscopic Dunham parameters Y01, Y11, Y21, Y31, Y02, and Y12 for both species, as well as Born-Oppenheimer breakdown (BOB) coefficients delta01 for Sn, Se, and Te. A direct fit of the same data sets to an appropriate radial Hamiltonian yielded analytic potential energy functions and BOB radial functions for the X 1Sigma+ electronic state of both SnSe and SnTe. Additionally, the magnetic hyperfine interaction produced by the dipolar nuclei 119Sn, 117Sn, 77Se, and 125Te was observed, yielding first determinations of the corresponding spin-rotation coupling constants.