The formation of nanostructures on the surface of GaAs under quasi-equilibrium conditions in a quasi-closed volume from saturated phosphor and indium vapors in the presence of a Au catalyst with growth according to the “vapor–liquid–crystal” mechanism is considered for the first time. The influence of the growth temperature and size of Au drops on the morphology and composition of the fabricated nanostructures is studied. Experimental data on the formation of Ga(In)AsP nanocrystals on GaAs substrates with various orientations are presented. It is established that the temperature growth range of the nanostructures when using this method is 540–640°C with a drop size from 30 to 120 nm. It is shown that the size of the catalyst drops substantially affects the morphology and growth rate of the fabricated nanostructures while their composition weakly depends on both the drop size and the substrate orientation.