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 1C, which provide the necessary template for overgrowing films at a higher temperature near 500 1C. 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 ¼ 0:5691 nm and a ¼ 0:3544 nm for a continuous 0.9 mm film and c ¼ 0:5700 nm and a ¼ 0:3533 nm for a columnar 1.6 mm 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. r 2005 Published by Elsevier B.V.