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Transmission electron microscopy is used to examine the structure and composition of In x Ga 1− x N nanorods grown by plasma-assisted molecular beam epitaxy. The results confirm a core–shell structure with an In-rich core and In-poor shell resulting from axial and lateral growth sectors respectively. Atomic resolution mapping by energy-dispersive x-ray microanalysis and high angle annular dark field imaging show that both the core and the shell are decomposed into Ga-rich and In-rich platelets parallel to their respective growth surfaces. It is argued that platelet formation occurs at the surfaces, through the lateral expansion of surface steps. Studies of nanorods with graded composition show that decomposition ceases for x ≥ 0.8 and the ratio of growth rates, shell:core, decreases with increasing In concentration.