Thermodynamic analysis was performed to investigate the coherent growth of GaAs 1-xN x thin films with low N content. In the present study, a new algorithm of the simulation code was developed to theoretically predict the relationship between solid composition and growth condition. This algorithm is applicable to wider varieties of combinations of gaseous sources than is the traditional algorithm. The system using trimethylgalllium (TMG), AsH 3, and NH 3 was analyzed with the new code, and the results showed that the required input partial pressure ratio of NH 3 to the group-V element is over 99% for incorporation of a small percent of N into a solid. It is difficult to incorporate N into the solid when the input V/III ratio is low, while in the case of a high input V/III ratio, stable growth with a small percent of N can proceed. In the case of coherently grown GaAs 1-xN x, the lattice constraint from the substrate would suppress the incorporation of nitrogen. On the other hand, a higher input Ga partial pressure ratio enhances the stable growth of GaAs 1-xN x with a small N content, though this condition tends to easily induce generation of dislocations. Furthermore, a much lower optimum N/As ratio in input gas can be achieved in the system with dimethylhydrazine (DMHy). This result confirms that the difference in gaseous sources has a great effect on N incorporation. When determining well-optimized experimental growth conditions, these influences including crystallinity should all be considered.