The dependence of the optical band gap of InNxSb1-x and GaNxSb1-x on nitrogen content has been calculated using an sp(3)s(*) tight-binding Hamiltonian in large supercell calculations that explicitly include the effects of allowing a random distribution of nitrogen atoms. We calculate for InNSb that the energy levels associated with nitrogen complexes consisting of two or three atoms mostly lie above the InNSb conduction band edge (CBE). The steady reduction in the band gap of InNSb with increasing N composition is then well described using a two-level band-anticrossing model. The calculated effective mass of electrons in InNSb also smoothly decreases with composition, as predicted by the band-anticrossing model, due to the steady closure of the band gap and weak mixing with the N states. For GaNSb the situation is dramatic: the band gap and optical properties are shown to be strongly affected and highly sensitive to the distribution of the nitrogen atoms. We find that there is a wide distribution of N levels lying close to and below the CBE. The higher-lying N states push the CBE down in energy, as in GaAs, but the large number of lower-energy N states mix in strongly with the conduction band edge states, severely disrupting the band edge dispersion in GaNSb.