Two In x Ga1-x N nanorod samples with graded In compositions of x = 0.5-0 (Ga-rich) and x = 0.5-1 (In-rich) grown by molecular beam epitaxy were studied using transmission electron microscopy. The nanorods had a wurtzite crystal structure with growth along [Formula: see text] and core-shell structures with an In-rich core and Ga-rich shell. Energy-dispersive x-ray analysis confirmed grading over the entire compositional range and showed that the axial growth rate was primarily determined by the In flux, and the radial growth rate by the Ga flux. There was no evidence of misfit dislocations due to grading, but the strain due to the lattice mismatch between the In-rich core and Ga-rich shell was relaxed by edge dislocations at the core-shell interface with Burgers vectors [Formula: see text] and [Formula: see text].