The electronic structure of GaN and AlN (0001) surfaces and modification by cesium (Cs) adsorption are investigated via ultra-violet and X-ray photoemission spectroscopy (UPS, XPS) and total yield spectroscopy. The electron affinity (EA) of the clean and ordered 1 X 1 surfaces is found to be equal to 3.3 and 1.9 eV for GaN and AlN, respectively. Cs adsorption (with the help of oxygen pre-treatment in the case of GaN) reduces EA on both surfaces by about 2.6-2.8 eV, leading to true negative electron affinity (NEA) in the case of AlN and effective NEA in the case of GaN. Total yield spectroscopy confirms NEA on both surfaces.