A space-angle synthesis (SAS) method is developed for the steady-state, two-dimensional transport of neutrons and secondary gamma rays from a point source of simulated nuclear-weapon radiation in air. The method is validated by applying it to the problem of neutron transport from a point source in air over a ground interface, and then comparing the results to those obtained by DOT, a discrete-ordinates code. In the method, the energy dependence of the Boltzmann transport equation is treated in the standard multigroup manner. The angular dependence is treated by expanding the flux in specially tailored trial functions and applying the method of weighted residuals that analytically integrates the transport equation over all angles. The trial functions used in the expansion are composed of combinations of selected trial solutions, the trial solutions being shaped ellipsoids that approximate the angular distribution of the neutron flux in one-dimensional space. Differences between DOT and SAS tissue-dose calculations at distances >60 m from the source were generally under 10% and decreased with increasing source or receiver height. Computer computational time was decreased by a factor of ∼7.