The pure rotational spectra of the X 2-SIGMA+ ground states of the SrOH and SrOD radicals have been observed in the laboratory using millimeter/submillimeter direct absorption spectroscopy. The lesser abundant isotopically substituted species, (SrOH)-Sr-86, has been observed as well. The molecules were produced in a Broida-type oven by the reaction of Sr metal vapor with either H2O2 or D2O2. The rotational and spin-rotation constants were determined for the radicals from a nonlinear least-squares fit to the data using a 2-SIGMA-Hamiltonian. The millimeter-wave measurements support the picture that strontium hydroxide is linear in its ground electronic and vibrational state.