A study by electron microscopy techniques of the structural and compositional properties of Al x Ga1-x N/GaN nanowire (NW) heterostructures on Si(111) is presented. Al x Ga1-x N depositions grown without catalyst by plasma-assisted molecular beam epitaxy were designed to form NWs in the range of 0.20<x<0.40 with different lengths and growth temperatures. The NWs exhibit a well-defined core-shell radial structure with a complex chemical distribution along and across the growth direction that finally affects the NW morphology. All the wires have an initial stage with a maximum Al content in the core slightly above the GaN/Al x Ga1-x N interface, which initially decreases exponentially with the NW height depending on the nominal Al content and the growth temperature. In longer NWs, this trend changes and evolves increasing both the Al/Ga ratio and the core diameter as well as sharpening the shell. Adatom surface kinetic differences and the geometrical shadow effect during the growth are the probable drivers of this behavior.