We present a theoretical study of the electronic structure and optical properties of free-standing GaN and AlN nanowires. We have implemented the empirical tight-binding method, with an orbital basis sp(3), that includes the spin-orbit interaction. The passivation of the dangling bonds at the free surfaces is also studied, together with the effects on the electronic structure of the nanowire. For both GaN and AlN nanowires, we have found a remarkable anisotropy of the optical absorption when the light-polarization changes, showing in the case of GaN a dependence on the nanowire size.