We present empirical tight-binding (TB) calculations of the electronic structure of GaP1-xNx and InyGa1-yAs1-xNx alloys with low nitrogen content (x<0.05) over the entire Brillouin zone. Following the method recently developed for GaAs1-xNx [Shtinkov et al., Phys. Rev. B 67, 081202 (2003)], we add to the TB basis an additional anion s orbital (s(N)) in order to account for the N-induced change of the electronic structure. The band structures of GaP1-xNx and InyGa1-yAs1-xNx are,calculated using an sp(3)d(5)s*s(N) TB parametrization. Our TB results are in excellent agreement with experimental and other theoretical data without introducing any additional fitting parameters, demonstrating that the developed method is a promising tool for modeling a wide range of dilute nitride materials and heterostructures. (C) 2004 American Vacuum Society