The surface termination, composition, and structure of the Cd-terminated CdS{0001}-(1 x 1) and S-terminated CdS{000 (1) over bar}-(1 x 1) surfaces have been determined using time-of-flight scattering and recoiling spectrometry (TOF-SARS), three-dimensional classical ion trajectory simulations, and low-energy electron diffraction (LEED). TOF-SARS spectra of scattered and recoiled ions plus fast neutrals using 4 keV Nef and Krf primary ions were used to determine the termination layer, surface periodicity, and possible reconstruction. Experimental and simulated results for both surfaces consistently show that neither (1 x 1) surface is reconstructed, there are two domains rotated by 60 degrees from each other, and there are steps on the surface. Oxygen and hydrogen impurities are present on the {0001}-(1 x 1) surface at a level of 18% and 1% of a monolayer, respectively; the surface periodicities of the O and H are similar to those of Cd and S, respectively. The {000 (1) over bar}-(1 x 1) surface also contains oxygen and hydrogen impurities at a level of 14% and <1% of a monolayer, respectively; they exhibit no periodicity and appear to be randomly distributed over the surface. These O and H impurities are present on the surfaces even at 1200 degrees C. These unreconstructed polar surfaces can achieve stability by bonding to impurities such as oxygen and hydrogen, thereby being autocompensated.