In this work, we present a second nearest neighbour sp(3)s* semi-empirical tight-binding theory to calculate the electronic band structure of heterostructures based on group III-N binary semiconductors and their ternaries. The model Hamiltonian includes the second nearest neighbour (2nn) interactions, the spin-orbit splitting and the nonlinear variations of the atomic energy levels and the bond length with ternary mole fraction. Using this sp(3)s* tight-binding approach, we investigated the electronic band structure of Al1-xGaxN/GaN and In1-xGaxN/GaN heterostructures as a function of composition and interface strain for the entire composition range (0 <= x <= 1). There is an excellent agreement between the model predictions and experiment for the principal bandgaps at Gamma, L and X symmetry points of the Brillouin zone for AlN, GaN and InN binaries and Al1-xGaxN and In1-xGaxN ternaries. The model predicts that the composition effects on the valence band offsets is linear, but on the conduction band offsets is nonlinear and large when the interface strain and deformation potential is large. (c) 2006 Published by Elsevier Ltd.