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 GaN1-xAsx, 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 0.170.2, 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 GaN1-xAsx alloys for various types of solar power conversion devices.