AbstractDiscussion of band gap behavior based on first principles calculations of the electronic band structures for several InN/GaN superlattices (SLs) (free-standing and pseudomorphic) grown along different directions (polar and nonpolar) is presented. Taking into account the dependence on internal strain and lattice geometry mainly two factors influence the dependence of the band gap, E _g on the layer thickness: the internal electric field and the hyb wells) is more important. We also consider mIn ridization of well and barrier wave functions. We illustrate their influence on the band gap engineering by calculating the strength of built-in electric field and the oscillator strength. It appears that there are two interesting ranges of layer thicknesses. In one the influence of the electric field on the gaps is dominant (wider wells), whereas in the other the wave function hybridization (narrow wells) is more important. We also consider mIn _0.33 Ga _0.67 N/nGaN SLs, which seem to be easier to fabricate than high In content quantum wells. The calculated band gaps are compared with recent experimental data. It is shown that for In(Ga)N/GaN superlattices it is possible to exceed by far the range of band gap values, which can be realized in ternary InGaN alloys.