Alloying is a commonly accepted method to tailor properties of semiconductor materials for specific applications. Only a limited number of semiconductor alloys can be easily synthesized in the full composition range. Such alloys are, in general, formed of component elements that are well matched in terms of ionicity, atom size, and electronegativity. In contrast there is a broad class of potential semiconductor alloys formed of component materials with distinctly different properties. In most instances these mismatched alloys are immiscible under standard growth conditions. Here we report on the properties of GaN _{1- x} As _x , a highly mismatched, immiscible alloy system that was successfully synthesized in the whole composition range using a nonequilibrium low temperature molecular beam epitaxy technique. The alloys are amorphous in the composition range of 0.17≪ x ≪0.75 and crystalline outside this region. The amorphous films have smooth morphology, homogeneous composition, and sharp, well defined optical absorption edges. The band gap energy varies in a broad energy range from ∼3.4 eV in GaN to ∼0.8 eV at x ∼0.85 . The reduction in the band gap can be attributed primarily to the downward movement of the conduction band for alloys with x ≫0.2 , and to the upward movement of the valence band for alloys with x ≪0.2 . The unique features of the band structure offer an opportunity of using GaN _{1- x} As _x alloys for various types of solar power conversion devices.