The O 1s photoabsorption (ion-yield) spectra of OH ((2)Pi(i),v"=0) and OD ((2)Pi(i),v"=0) radicals have been studied in the gas phase for the first time. Spectroscopic parameters for the O 1s-->pi excited (2)Sigma(+) state of OH and OD, observed at similar to525.8 eV, have been obtained from a Franck-Condon analysis comparing the spectra of both molecules. The lifetime width of this state has been measured as Gamma=147+/-11 meV and Gamma=156+/-7 meV for OH and OD, respectively. Excellent quantitative agreement is found between the experimental spectroscopic parameters r(e), omega(e), and T-0, measured in this work for the (2)Sigma(+) state and recent theoretical results obtained for OH by high-level ab initio calculations. The spectroscopic parameters predicted by the equivalent-core model are close to the experimental values within a few percent. This model therefore provides an accurate description of the lowest-lying excitation process in both OH and OD molecules.