We present a detailed investigation of the mechanisms at play for the incorporation of In and Mg on the GaN(0001) surface during plasma-assisted molecular beam epitaxy. First, we have studied the kinetics of In desorption in the presence of Mg either without or with N supply from the plasma cell by quadrupole mass spectrometry in the line of sight. Second, we have explored the effect of Mg doping at a different time along the cycle of (InN/GaN) supply repeated 10 times to form (In,Ga)N/GaN superlattices (SLs). By the complementary ex situ investigation of these SLs by x-ray diffraction and secondary ion mass spectrometry, we found that in the monolayer-thick (In,Ga)N layer, the In content was maximized when Mg was not supplied simultaneously to In, but it drastically decreased otherwise. In contrast, the Mg concentration strongly increased in the (In,Ga)N monolayers compared to the GaN barriers. We attribute …