Abstract The heteroepitaxy of In-face InN on Ga-face GaN (0 0 0 1) by nitrogen RF plasma source molecular beam epitaxy, using a two-step growth process, has been investigated. InN nucleation is enhanced at low substrate temperatures and smooth continuous nucleation layers can be grown at 300–350 °C, which provide the necessary template for overgrowing films at a higher temperature near 500 °C. Porous columnar InN structures are grown without the low-temperature nucleation layer, exhibiting a multiplied growth rate along the c-axis. The continuous InN/GaN (0 0 0 1) films are under tensile residual stress at room temperature attributed to the different thermal expansion of InN and GaN. Typical lattice constants are c = 0.5691 nm and a = 0.3544 nm for a continuous 0.9 μm film and c = 0.5700 nm and a = 0.3533 nm for a columnar 1.6 μm epilayer. A difference in the density of misfit dislocations at the InN/GaN (0001) interface between columnar and continuous films was observed, in agreement with measurements of the films’ lattice constants.