Electron cyclotron resonance-metalorganic molecular beam epitaxy has been used to deposit GaN and GaAsxN1-x layers on various substrates. This paper will report on the structural characterization of this material, as measured by x-ray diffraction and cross-sectional transmission electron microscopy. GaAsN1-x layers grown on GaAs appear to be cubic while those grown on GaP are surprisingly hexagonal. The hexagonal phase is also observed under some growth conditions in material grown on GaAs, however, the cubic phase can be obtained by optimizing the parameters which affect the initial nucleation. Conditions such as pre-deposition annealing and growth temperature are critical in determining the phase and crystallinity of the resulting layers. Because of the reduced mismatch between GaN and GaP, the cubic phase of GaN can be more easily nucleated on GaP substrates than on GaAs wafers using similar growth conditions. However, the films under all growth conditions are fine-grained polycrystalline. The impact on film quality of various strain dissipation schemes, such as grading the group V species across the As (or P)-N interface, will also be discussed.