An assessment of the calculational accuracy of the discrete-ordinates codes, PALLAS-2DCY and DOT-III, has been performed for gamma-ray transport through air from a 60Co point isotropic source. The first collision source technique was used in the calculations. The results were compared with the measured exposure dose rates near the ground surface. Also, the ratio of the dose rates by gamma rays incident on and reflected from the ground was compared between the calculations. In addition, the calculated angular fluxes were examined. It is shown that the use of a truncated Legendre polynomial expansion implemented on DOT-III is not sufficient for calculations of gamma-ray scattering in air, while the direct application of the Klein-Nishina formula on PALLAS-2DCY is adequate to the calculations. Both two-dimensional transport codes, however, are useful for calculating the gamma-ray transport through air with a practical accuracy. PALLAS-2DCY requires one-fifth the central processor unit time as DOT-III.