Density-functional theory calculations were carried out for various surface reconstructions of atomically ordered thin films of In_xGa_1−xAs on the InP(001) substrate for compositions close to x=1/2. In addition to the known (n×3) and (2×4) reconstructions, a gallium-rich zeta(4×2) reconstruction, so far only observed for binary arsenides, is predicted. Moreover, the possibility of a c(4×4) reconstruction, either purely terminated by As-As dimers or mixed with heterodimers, as well as the possible occurrence of heterodimers in other reconstructions have been investigated. From our calculated film formation energies, these reconstructions are expected to play a minor role for In_xGa_1−xAs films under thermodynamic equilibrium conditions. For the surface-induced atomic ordering in the In_xGa_1−xAs films, our calculations are in line with known trends for In_xGa_1−xP alloys. In general, the energetic preference for near-surface ordering in the In_xGa_1−xAs system is found to be somewhat weaker than in the In_xGa_1−xP system.