A modified electron cyclotron resonance plasma source, allowing optically active GaN thin films at growth rates up to 1 mu m per h, was utilized in a molecular beam;epitaxy environment for Mg doping studies of GaN. The effect of the growth parameters on the Mg incorporation was studied using secondary ion mass spectroscopy and Hall measurements. We found that Mg does not incorporate when GaN is grown under Ga-rich conditions, independently of the Mg flux, in the temperature range of 700-800 degrees C. Only N-rich growth conditions allow measurable Mg incorporation; This incorporation increases with decreasing Ga cell temperature. Furthermore, under N-rich growth conditions, the Mg content is more sensitive to the lowering of the substrate temperature than to the increase of the Mg cell temperature.