Amorphous GaN models are obtained from first principles simulations. We compare four a-GaN models generated by "melt-and-quench" and the computer alchemy method. We find that most atoms tend to be four-fold, and a chemically ordered continuous random network is the ideal structure for a-GaN albeit with some coordination defects. Where the electronic structure is concerned, the gap is predicted to be less than 1.0 eV, underestimated as usual by a density functional calculation. We observe a highly localized valence tail and a remarkably delocalized exponential conduction tail in all models generated. Based upon these results, we speculate on potential differences in n and p type doping. The structural origin of tail and defect states is discussed. The vibrational density of states and dielectric function are computed, and seem consistent with experiment.