Thin InN and GaN/InN films were grown on oxygen-polar (O)(000-1) and zinc-polar (Zn)(0001) zinc oxide (ZnO) by plasma-assisted molecular beam epitaxy (PAMBE). The influence of the growth rate (GR) and the substrate polarity on the growth mode and the surface morphology of InN and GaN/InN was investigated in situ by reflection high-energy electron diffraction (RHEED) and ex situ by atomic force microscopy (AFM). During InN deposition, a transition from two dimensional to three dimensional (2D-3D) growth mode is observed in RHEED. The critical thickness for relaxation increases with decreasing GR and varies from 0.6 ML (GR: 1.0 ML/s) to 1.2 MLs (GR: 0.2 ML/s) on O-ZnO and from 1.2 MLs (GR: 0.5 ML/s) to 1.7 MLs (GR: 0.2 ML/s) on Zn-ZnO. The critical thickness for relaxation of GaN on top of 1.2 MLs and 1.5 MLs thick InN is close to zero on O-ZnO and 1.6 MLs on Zn-ZnO, respectively.