In this work, the electronic band structure of III (In, Al, Ga) - V (N, As, Sb) compounds and their ternary alloys have been investigated by density functional theory (DFT) within generalized gradient approximation (GGA) and empirical tight binding (ETB) calculations, respectively. The present DFT-GGA calculations have shown direct band gap structures in zinc-blende phase for InN, InAs, InSb, GaN, and GaAs. However, indirect band gap structures have been obtained for cubic AlN, AlSb and AlAs com- pounds / here, the conduction band minima of both AlN and AlAs are located at X symmetry point, while that of AlSb is at a position lying along Gamma- X direction. An important part of this work consists of ETB calculations which have been parameterized for sp3d2 basis and nearest neighbor interactions to study the band gap bowing of III(In / Al)- V(N / As / Sb) ternary alloys. This ETB model provides a satisfactory electronic properties of alloys within reasonable calculation time compared to the calculations of DFT. Since the present ETB energy parameters reproduce successfully the band structures of the compounds at &iexcl / and X symme- try points, they are considered reliable for the band gap bowing calculations of the ternary alloys. In the present work, the band gap engineering of InNxAs1&iexcl / x, InNxSb1&iexcl / x, InAsxSb1&iexcl / x, Al1&iexcl / xInxN, Al1&iexcl / xInxSb and Al1&iexcl / xInxAs alloys has been studied for total range of constituents (0 &lt / x &lt / 1). The downward band gap bowing seems the largest in InNxAs1&iexcl / x alloys among the alloys considered in this work. A metallic character of InNxAs1&iexcl / x, InNxSb1&iexcl / x and InAsxSb1&iexcl / x has been ob- tained in the present calculations for certain concentration range of constituents (N / As) as predicted in the literature. Even for a small amount of contents (x), a decrease of the electronic e&reg / ective mass around &iexcl / symmetry point appears for InNxAs1-x, InNxSb1-x and InAsxSb1-x alloys manifesting itself by an increase of the band curvature. The calculated cross over from indirect to direct band gap of ternary Al alloys has been found to be consistent with the measurements. As a last summary, the determinations of the band gaps of alloys as a function of contents, the concentration range of con- stituents leading to metallic character of the alloys, the change of the electronic effective mass around the Brillioun zone center (Gamma) as a function of alloy contents, the cross over from indirect to direct band gap of the alloys which are direct on one end, indirect on the other end, are main achievements in this work, indispensable for the development of mate- rials leading to new modern circuit components.