The pure rotational spectra of 41 isotopic species of PbSe and PbTe have been measured in their X 1Sigma+ electronic state with a resonator pulsed-jet Fourier transform microwave spectrometer. The molecules were prepared by laser ablation of suitable target rods and stabilised in supersonic jets of noble gas. Global multi-isotopologue analyses yielded spectroscopic Dunham parameters Y01, Y11, Y21, Y31, Y02, and Y12 for both species, as well as effective Born-Oppenheimer breakdown (BOB) coefficients delta01 for Pb, Se and Te. Unusual large values of the BOB parameters for Pb have been rationalized in terms of finite nuclear size (field shift) effect. 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 PbSe and PbTe. Additionally, the magnetic hyperfine interactions produced by the uneven mass number A nuclei 207Pb, 77Se, 123Te, and 125Te were observed, yielding first determinations of the corresponding nuclear spin-rotation coupling constants.